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1065 


1065 


ELEMENTARY  OPTICS 

AND 

APPLICATIONS  TO  FIRE  CONTROL 
INSTRUMENTS 


PREPARED  UNDER  THE  DIRECTION  OF 
THE  CHIEF  OF  ORDNANCE 


May,  1921 


WASHINGTON 

OOVERNMKNT  PRINTING  OFFICE 

1922 


PHWCS  OK"- 


ilF  ?is 

fMYSICS  t)EPT, 


WAR  DEPARTMENT, 

Washington,  3Iay  10,  1921. 

The    following    publication,    entitled    ''Elementary    Oj)tics    and 
Applications    to    Fire  Control    Instruments,"    is    published    for    the 
information  and  guidance  of  all  concerned. 
\mi.\,  A.  G.  o.] 

By  order  of  the  Secretary  of  War: 

PEYTOX  Q.  MARCH, 

Major  General,  Chief  of  Staff. 
Official: 

P.  C.  HARRIS, 

The  Adjutant  General.  '-■  : 
(3) 


810829 


:n. 


PREFACE. 


The  aim  in  the  jDreparation  of  this  pamplilet  lias  been  to  provide 
a  handbook  of  apphed  optics  and  optical  instruments  suitable  for  use 
as  a  textbook  in  the  Army  training  schools ,  and  for  the  information 
of  the  officers  and  men  who  use  optical  fire  control  apparatus. 

In  the  selection  of  material  no  attempt  has  been  made  to  produce 
an  exhaustive  treatise.  It  has  rather  been  the  purpose  to  treat  more 
fully  those  phases  of  the  subject  which  are  not  dealt  with  in  the  books 
ordinarily  available,  or  which  are  particularly  characteristic  of  fire 
control  instruments,  and  to  avoid  the  unnecessary  duplication  of 
material  which  is  already  accessible  in  elementary  textbooks  so  far 
as  is  possible  without  the  undue  sacrifice  of  completeness. 

For  the  reader  who  desires  more  complete  information,  the  follow- 
ing books,  all  of  which  are  available  in  English,  are  recommended: 

Crude:  Theory  of  Optics.  Translated  by  I\Iann  and  Millikan.  Longmans,  Green 
&  Co. 

Edser:  Light  for  Students.     Macmillan  &  Co.  (Ltd.),  London. 

Nutting:  Outlines  of  Applied  Optics.     P.  Blaldston's  Son  &  Co.,  Philadelphia,  Pa. 

Taylor:  A  System  of  Applied  Optics.     Macmillan  &  Co.  (Ltd.),  London. 

Steinheil  and  Voit:  Applied  Optics.  Translated  in  two  volumes  by  P'rench. 
Blackie  &  Son  (Ltd.),  London. 

Southall:  The  Piinciples  and  Methods  of  Geometrical  Optics.     The  ]\Iacmil]an  Co. 

Gleichen:  The  Theory  of  Modern  Optical  Instruments.  Translated  by  Emsley  and 
Swjdne.     H.  AL  Stationery  Office,  London. 

Von  Rohr:  The  Formation  of  Images  in  Optical  Instruments.  Translated  by  R. 
Kanthack.     H.  M.  Stationery  Office,  London. 

Hovestadt:  Jena  Glass.  Translated  by  J.  IJ.  ct  A.  Everett.  Macmillan  &  Co. 
(Ltd.),  London. 

(4) 


TABLE  OF  CONTENTS. 


Page. 

Tlio  reflertion  and  refraction  of  light 7 

T>aw  of  reflection — Law  of  refraction — Absolute  and  relative  index — Re- 
flection fi-om  metallic  surface — Reflection  from  transparent  surface — 
Total  reflectioji. 

The  dispersion  of  light 10 

De\iation  by  a  prism — Minimum  deviation — Production  of  spectra — 
Physical  nature  of  light — Spectral  lines — ^fethod  of  specif>dng  optical 
glass. 

Atmospheric  refraction ^ . .         13 

Path  of  light  in  a  nonhomogeneous  meditim — Influence  of  refraction  ttpon 
the  visibility  of  distant  objects — Effects  due  to  irregular  refraction  by 
atmosphere. 

Plajie  mirrors IG 

Image  of  a  point — Image  of  an  extended  object — Reversion — Image  pro- 
duced by  two  successive  reflections — Image  prodiiced  by  two  perpen- 
dicular mirrors. 

Prisms 20 

Measiuing  wedge — Achromatic  prism^ — Right-angle  prism — Porro  prism, 
first  and  second  type — Right-angle  prism  with  roof — Rotating  prism — 
Brashear-Hastlngs  prism — -One-piece  erecting  prism  with  roof — Aiming- 
circle  erecting  system — Triple  mirror — Penta  prism — Penta  reflector — 
Rhomboidal  prism. 

The  spherical  reflecting  surface 27 

Image  of  an  axial  point — Focal  length — Searchlight  mirror — Parabolic 
reflector. 

The  spherical  refracting  surface 30 

Image  of  an  axial  point. 

The  thin  lens 31 

Image  of  an  axial  point — Image  of  an  extended  object — Convergent  and 
di^•ergent  lenses — Simple  magnifying  lenses — Di^'erging  lens  in  the  floor 
of  an  airplane — <."ylindrical  lenses. 

Tliick  lenses  and  combinations 37 

Location  of  principal  points— Equivalent,  back  and  front  focal  lengths — 
Principal  planes — Two  thin  lenses  in  contact — Two  separated  lenses. 

The  aberrations  of  a  lens -40 

Effect  of  aberrations  upon  the  image — Spherical  aberration — Chromatic 
aberration — .\stigmatism — Coma — Curvature — Distortion. 

Resolving  power 4() 

The  telescopic  system 47 

Image  of  an  axial  point — Image  of  an  extra-axial  point — Magnifying  jiower— 
Galilean  type  of  telescope — Reflecting  telescope. 

The  telescope  and  tlie  eye 51 

Parts  of  the  eye — Myopia — Hypermetropia — Astigmatism — Field  of  A-iew — 
Combined  action  of  eye  and  telescope — Focusing  of  telescope  for  the 
individual  eye — Depth  iji  the  image — Stereoscopic  vision — Radius  of 
stereoscopic  vision. 

C5) 


6 

Page. 

The  components  of  the  telescope 5G 

(Objectives — Eyepieces —Reticules  Adjustments  necessary  for  focusing— 
Parallax — Fixed-focus  telescopes. 

The  telescope  with  an  erecting  system 62 

Lens  erecting  system — Different  types  of  prism  erecting  systems. 

The  field  of  view  and  brightness  of  image f!7 

True  and  apparent  field     Position  of  the  eye — Exit  pupil — ^Night  glasses. 

The  selection  and  use  of  a  telescope 70 

Desirable  optical  properties  for  hand  telescopes — Focusing  of  the  telescope — 
Tests  of  definition — Tests  for  film  on  reticule. 

The  optical  characteristics  of  service  fire-control  instrumejits 73 

Telescopic  musket  sight,  model  1913— French  aiming  circle— Macliine-gun 
panoramic  sight— Azimuth  instrument,  model  1918 — Azimuth  instru- 
ment, model  1910 — Observation  telescope,  "  Longue  Aaie  Monoculaire  " — 
2-inch  telescopic  sight — 3-inch  telescopic  sight — Lewis  depression  ])osi- 
tion  finder— Telescopic  sight  for  tank  gun— Telescopic  musket  sight- 
Telescopic  sight  for  37-mm.  infantry  gun— Officer's  trench  periscope 
No.  10;  battery  commander's  periscope — Periscopic  azimuth  instru- 
ment, model  1918 — Right-angle  telescope — Panoramic  sight,  4  power — 
Panoramic  telescope,  4  and  10  power — Binocular,  type  EE — Battery 
commander's  telescope— Aiming  circle,  model  1916. 

The  collimator 82 

Principles  of  collimator— Tj^pes  of  construction— Use  of  Collimator- 
Collimator  on  Michelin  bomb  sight. 

The  coincidence- type  self-contained  range  finder 85 

Fundamental  triangle — Optical  system  of  range  finder — Types  of  field — 
Measuring  wedge — Adjusting  wedge. 

The  construction  of  the  range  finder 89 

Range  scale— Rotating  compensating  prisms— Equal-magnification  lens  - 
Ocular  prism— Optical  tube — Astigmatizer— Optical  characteristics  of 
range  finders  used  by  the  service — Transmission  of  a  range  finder. 

The  azimuth  type  of  coincidence  range  finder 93 

The  stereoscopic  range  finder 94 

The  errors  of  the  range  finder 96 

Accidental  errors— Table  showing  effect  on  range  readings— Systematic 
errors. 

The  infinity  adjustment  of  the  range  finder 

By  known  range — By  Tise  ,of  celestial  object— Adjusting  lath — Errors  of 
adjusting  lath— Barr  &  Stroud  type  of  internal  adjustment— Internal 
adjustment  by  triple  mirrors— Zeiss  absolute  internal  adjustment. 


99 


ELEMENTARY  OPTICS  AND  APPLICATIONS  TO  FIRE-CONTROL 
INSTRUMENTS. 


THE   REFLECTION   AND    REFRACTION    OF    LIGHT. 

The  path  of  a  ray  of  light  traveling  in  a  homogeneous  medium  is  a 
straight  line.  When,  however,  a  ray  is  incident  upon  a  surface  sep- 
arating two  media,  the  path  in  general  is  no  longer  straight.  The 
ray  is  divided  into  two  portions,  one  of  which  does  not  enter  the 
second  medium  but  is  reflected  back  into  the  first,  while  the  other 
continues  into  the  second  medium  but  is  refracted  and  travels  in  a 
different  direction. 

If  a  normal  is  erected  to  the  surface  at  the  point  where  it  receives 


the  incident  rav,  the  angles  which  the  incident, 


refracted  and  re- 
respectivoly,    the 


fleeted  rays  make  with  the   normal    are    termed. 

angles  of  incidence,  refraction,  and 

reflection.     The  laws  of  reflection 

and   refraction,    which   state    the 

relations   existing   between    these 

angles,  are  the  fundamental  laws 

upon  which  instrument  design  is 

based. 

The  law  of  reflection. — The  angles 
of  incidence  and  reflection  lie  in 
the  same  plane  and  are  equal. 

The  law  of  refraction. — The 
angles  of  incidence  and  refraction 
lie  in  the  same  plane,  and  the  sine 
of  the  angle  of  incidence  divided  by 
the  sine  of  the  angle  of  refraction 
is  equal  to  a  constant  n  characteristic  of  the  two  media  and  termed 
the  index  of  refraction  of  the  second  medium  with  respect  to  the 
first.  These  two  laws  are  sufTicient  to  determine  the  path  of  a  ray 
when  the  initial  path  and  boundary  and  indic(>s  of  refraction  for  each 
medium  are  given.  In  mathematical  form  they  may  be  expressed 
])y  the  two  e([uations: 

sin  ('  =  /(  sin  i'  (1) 

i  =  i"  (2) 

where  i  is  the  angle  of  incidence,  /"'  the  angle. of  refraction,  and  i" 


the  angle  of  reflection. 


(7) 


«% 


^ 


8 

The  refraction  and  reflection  of  a  ray  of  light  is  ilkistrated  in  figure 
1.  AB  is  the  trace  of  the  refracting  surface  which  separates  the  first 
and  second  medium.  CN  is  the  incident  ray  incident  upon  the  re- 
fracting surface  at  N.  It  is  there  divided  into  two  portions,  the 
reflected  portion  which  remains  in  the  first  medium  traveling  along 
the  line  ND  and  the  refracted  portion  which  enters  the  second  me- 
dium, is  deviated  and  travels  along  the  line  NE.  The  angle  d,  be- 
tween the  refracted  ray  and  the  incident  ray  produced,  is  termed  the 
"angle  of  deviation"  and  is  the  angle  through  which  the  ray  is  bent 
from  its  original  path.  From  the  drawing  it  is  evident  that  it  is 
equal  to  i  —  i'.  It  should  be  noted  that  if  a  ray  is  incident  normally 
upon  a  surface  sin  i  is  zero,  and  by  the  equation  (1),  sin  i'  is  also  zero. 
Angles  i  and  i'  are  equal  and  the  ray  is  not  deviated. 

The  constant  n  in  equation  (1)  is  the  index  of  refraction  of  the  sec- 
ond medium  with  respect  to  the  first  and  is  a  relative  index.  The 
index  of  refraction  of  any  substance  with  respect  to  a  vacuum  is 
termed  the  ''absolute  index."  If  n^  and  lu  are  the  absolute  indices 
of  refraction  of  two  substances,  the  value  of  ri,  the  index  of  the 
second  with  respect  to  the  first,  is  "'/„,.  Equation  (1)  is  therefore 
often  written  in  the  more  symmetrical  form: 

n^  sin  1  =  712  sin  /'  (3) 

From  this  equation  it  is  seen  that  the  index  of  a  first  medium  with 
respect  to  a  second  is  the  reciprocal  of  the  index  of  the  second  with 
respect  to  the  first. 

The  absolute  index  of  air  at  atmospheric  pressure  is  1.00029.  The 
absolute  index  and  index  with  respect  to  air  are  commonly  consid- 
ered identical,  a  relationship  which  would  be  strictly  true  if  the  index 
of  air  were  1  instead  of  1.00029.  The  indices  of  refraction  of  the 
types  of  glass  used  in  optical  instruments  lie  between  1.5  and  1.7. 

Of  two  substances,  the  one  which  has  the  greater  absolute  index  of 
refraction  is  said  to  be  the  more  dense  optically.  When  a  ray  passes 
from  a  less  dense  to  a  more  dense  medium,  it  is  bent  toward  the  nor- 
mal as  shown  in  figure  1.  If  bent  away  from  the  normal,  it  is  passing 
from  a  more  dense  to  a  less  dense  medium. 

In  the  above,  it  has  been  tacitly  assumed  that  the  surface  con- 
cerned is  a  polished  surface.  If  the  surface  is  rough,  as  for  example 
the  ground  surface  of  glass,  and  a  beam  of  light  falls  upon  it,  rays 
falling  upon  different  portions  of  the  surface  after  reflection  or  re- 
fraction do  not  proceed  in  common  directions.  This  is  not  because 
the  laws  as  stated  above  do  not  hold.  Rather,  the  rough  surface  is 
to  be  considered  as  composed  of  numerous  elementary  surfaces 
turned  in  different  directions,  at  each  of  which  regular  reflection  and 
refraction  takes  place.  The  net  result  of  the  many  small  surfaces  is 
the  scattering  of  the  beam.     Such  reflection  and  refraction  is  termed 


9 


"irregular"   or  " diffuse, "  in  contradistinction   to  regular  reflection 
and  refraction  at  ])olislied  surfaces. 

The  magnitudes  of  the  reflected  and  refracted  i)ortions  of  the  light 
are  dependent  upon  the  characteristics  of  the  surface,  the  material 
of  which  it  is  made  and  the  angle  of  incidence.  In  general  a  polished 
metallic  surface  reflects  the  larger  portion  of  the  light.  The  refracted 
part  which  is  very  small  is  entirely  absorbed  before  it  penetrates  very 
far  into  the  metal.  That  some  of  the  light  does  actually  enter  the 
metal  is  shown  by  the  fact  that  metal  in  very  thin  films  is  transparent. 
A  freshly  polished  silver  surface  may  reflect  as  much  as  98  per  cent 
of  the  incident  light. 

If  we  have  a  polished  transparent  surface,  the  amount  of  reflected 
light  varies  with  the  index  of  refraction  of  the  material  and  the  angle 
of  incidence.  For  a  surface  sep- 
arating glass  and  air  from  4  to  6  per 
cent  is  reflected  when  the  angle  of 
incidence  is  small,  that  is,  when 
the  light  falls  upon  the  surface 
at  nearly  normal  incidence.  The 
amount  reflected  increases  with 
the  angle  of  incidence  until  at  graz- 
ing incidence  all  is  reflected. 

Equation  (3)  may  be  written  in 
the  form: 


sm  t  =  sm  I  . 


(4) 


■Angle  of  incidence  less 
angle 


If  the  ray  is  traveling  within  a       i 
dense  medium  and  falls  upon  a 
surface  bounding  a  less  dense  medium,  the  quotient  "'/„,  is  greater 
than  1. 

It  is  seen  that  under  such  circumstances  there  may  be  values  of 
sin  i,  for  which  equation  (4)  indicates  a  value  of  sin  /'  greater  than 
1,  for  which  obviously  there  is  no  corresponding  angle.  This  wnll  be 
the  case  for  any  value  of  i  such  that  sin  i  is  greater  than  ""/„,.  In 
this  case  there  is  no  refracted  ray  but  all  the  light  is  reflected,  the 
ordinary  law  of  reflection  holding.  Such  reflection  is  termed  ''  total 
internal  reflection."  For  any  angle  i,  the  sine  of  which  is  less  than 
"Vn,.  we  have  both  reflection  and  refraction.  The  angle,  the  sine  of 
which  is  "V„„  is  termed  the  ''critical  angle."  For  this  angle  the 
refracted  ray  makes  an  angle  of  90  degrees  with  the  normal  f that  is, 
it  proceeds  in  the  second  medium  along  the  boundary  surface.  Fig- 
ures 2,  3,  and  4  show  the  course  of  a  ray  of  light  incident  respectively 
at  angles  less  than,  equal  to,  and  greater  than  the  critical  angle. 
The  lettering  is  the  same  as  in  figure  1 . 


10 


The  light  is  travehng  from  a  more  dense  to  a  less  dense  medium. 
Accordingly,  in  figure  2  the  ray  after  refraction  is  bent  from  the 
normal.  In  figure  3  the  ray  is  incident  at  the  critical  angle  and  the 
refracted  ray  travels  along  NB.  In  figure  4  we  have  total  internal 
reflection  and  there  is  no  refracted  ray.  All  the  light  is  reflected  at 
AB  and  travels  in  the  direction  ND. 

For  a  surface  separating  glass  and  air,  if  the  index  of  refraction 
is  1.5,  the  critical  angle  is  42°,  since 

If,  therefore,  a  ray  of  light  traveling  in  glass  incident  on  a  surface  sepa- 
rating glass  and  air  makes  an  angle  with  the  normal  greater  than 
42°,  none  of  the  light  will  pass  into  the  air,  but  all  of  it  will  be  reflected. 


Fig.  3.— Angle  of  incidence  equal  to  critical  angle. 


D  B 

Fig.  4.— Angle  of  incidence  greater  than  critical 
angle. 


THE    DISPERSION   OF   LIGHT. 

Let  FGH,  figure  5,  be  the  cross  section  of  a  prism  of  glass  bounded 
by  the  polished  faces  FG  and  FH.  The  angle  a  between  these  faces 
is  termed  the  refracting  angle  of  the  prism.  Since  the  rays  of  light 
to  be  dealt  with  are  not  incident  upon  the  face  GH,  its  location  or  the 
condition  of  its  surface  is  not  essential.  The  ray  AB  incident  at  B 
is  deviated  at  the  first  surface  through  the  angle  i^  —  i'i,  and  at  the 
second  face  is  turned  further  through  the  angle  i'^  —  i^.  If  d  is  the 
angle  between  the  entrant  ray  AB  and  the  emergent  ray  CD,  then 
d  =  i^  —  i\-\-i\--i.,  (5) 

We  have  the  following  relations  existing  between  the  four  angles 
of  the  right-hand  member: 

sin  I,  =  11  sin  i\ 


11 

The  value  of  d  is  a  function  of  a,  n,  and  i^.  For  a  given  prism  a 
and  n  are  constant  and  d  then  is  a  function  of  i^.  It  can  be. shown  by 
differentiation  that  d  is  a  minimum  for  the  value  of  i^  which  makes 
^l  and  i\  equal.  The  ray  then  travels  through  the  prism  in  a  sym- 
metrical manner,  as  shown  in  figure  6.  This  minimum  value  of  d 
which  we  shall  denote  by  do  is  termed  the  ''angle  of  least  deviation." 
Its  value  may  b(»  determined  ])y  the  equation 


sin  2  (a+do) 


(0) 


It  is  by  means  of  this  equation  that  the  index  of  refraction  of  a  prism 
is  commonly  deter- 
mined. The  angles  F 
do  and  a  are  meas- 
ured by  means  of  a 
spectrometer  and 
the  value  of  n  ob- 
tained by  the  substi- 
tution of  the  values 
in  the  above  equa- 
tion. 

We  have  thus  far 
spoken  of  a  prism  or 
piece  of  glass  as 
though  it  has  but  a 
single  index  of  re- 
fraction. The  true 
situation  is  not  so 
simple.  The  index 
of  refraction  takes 
on  a  different  value 
for  each  color. 

This  is  illustrated  in  figure  7.  White  light  is  not  to  be  considered 
as  a  fundamental  type  of  light,  but  is  rather  a  composite  mixture 
of  all  colors  in  a  certain  definite  proportion.  Suppose  AB  represents 
a  ray  of  such  light.  When  it  falls  upon  the  first  face  of  the  prism  at 
B,  each  color  of  which  the  ray  is  composed  is  bent  through  a  differ- 
ent angle  as  the  indices  of  refraction  for  the  different  colors  are 
different.  Consequently  the  beam  is  spread  out  fanwise,  as  indi- 
cated with  the  red  bent  the  least,  the  blue  the  most,  and  the 
other  colors  in  intermediate  positions.  At  the  second  face  of  the 
})rism  the  colors  are  still  more  widely  separated  and  if  the  beam 
is  allowed  to  fall  on  a  white  surface  we  obtain  a  long  colored  strip, 
red  at  one  end  and  blue  at  the  other.  Such  a  colored  .band  is 
termed  a  '"spectrum."     Tl:e  breaking  up  of  the  original  beam  into  its 


Deviation  of  ray  by  a  prism. 


12 


phenomena  are  propagated. 


separate  colors  is  said  to  be  due  to  the  dispersion  of  the  prism,  which 
is  anotlier  term  for  the  variation  of  index  with  color. 

It  has  been  shown  that  light  is  periodic  in  nature  and  is  })ropagated 
as  waves  in  a  manner  analogous  in  some  respects  to  the  propagation 
of  sound.  In  the  case  of  sound  the  waves  are  air  waves  and  the 
pitch  of  the  sound  depends  upon  the  frequency  of  the  waves.  We 
know  that  light  travels  through  a  vacuum  and  it  is  therefore  evident 
that  the  waves  do  not  depend  uj)on  the  air  for  propagation.  It  is 
considered  that  the  light  waves  are  waves  transmitted  by  a  hypo- 
thetical substance  termed  the  "  ether,"  which  is  assumed  to  occupy  all 
space  including  even  that  occupied  by  matter  and  which  is  the 
medium   by  which   optical,  electrical,   magnetic,   and   gravitational 

Light  of  different  colors  differs  only  in 
the  frequency  with 
which  the  waves 
succeed  each  other; 
that  is,  light  differ- 
ing in  color  differs 
in  a  manner  analo- 
gous to  tha  t  in  which 
tones  of  different 
pitch  differ.  For 
the  blue  light,  the 
frequency  is  higher 
and  the  wave  length 
shorter  than  for  the 
red. 

An  examination 
of  the  spectrum  pro- 
duced by  an  incan- 
descent body  shows 
that  it  is  made  up, 
not  of  a  definite 
number  of  distinct  colors,  but  that  no  two  parts  are  the  same  and  that 
different  portions  blend  into  each  other  by  passing  through  a  large 
number  of  intermediate  colors.  This  indicates  that  the  frequency 
of  the  light  varies  continuously  from  one  end  of  the  spectrum  to 
the  other. 

The  spectrum  of  the  sun  contains  numerous  dark  lines  superposed 
on  the  continuous  background.  These  dark  lines  correspond  to  fre- 
quencies which  are  absorbed  by  the  atmospheres  of  the  sun  and  earth 
and  do  not  reach  the  observer.  As  the  relationship  between  these 
lines  and  the  colors  of  the  spectrum  are  invariant  the  lines  are  con- 
venient "landmarks"  for  designating  parts  of  the  spectrum  with 
pre(;jJ9Jyn.     These  lines  have   been   designated   by  letters   and   the 


G' ^H 

Fig.  6.— Path  of  minimum  deviation  through  a  prism. 


13 

C,  D,  F,  and  G'  linos  are  the  ones  commonly  referred  to  in  optical 
computations.  The  D  line  lies  in  the  yellow  portion  of  the  spectrum 
and  is  near  the  region  of  greatest  luminosity,  i.e.,  for  light  of  approxi- 
mately this  color  the  greatest  reaction  upon  the  eye  is  produced  in 
proportion  to  the  energy  present. 

The  C  and  F  lines  lie  on  either  side  of  the  D  line  in  the  red  and  blue- 
green  and  sufficiently  near  the  ends  of  the  visible  spectrum  to  be 
suitable  for  use  in  computations  carried  on  to  determine  whether  an 
optical  system  is  satisfactorily  corrected  for  the  entire  range  of  color. 
If  the  instrument  is  for  photographic  purposes,  the  G'  line,  further 
in  the  violet  than  the  F  line,  is  used  in  making  the  corrections,  as  the 
photographic  emulsion  is  more  sensitive  to  the  blue  end  of  the 
spectrum. 

In  selecting  glass  for  use  in  a  telescope  it  is  important  to  know  the 
index  of  refraction  for  the  C,  D,  and  F  lines.  The  color  to  which  an 
index  refers  is  indicated  by  a  subscript  as  Hd  referring  to  the  D  line. 
The  quantity  np-iic  is  termed  the 
mean  dispersion,  as  this  quantity  is  a 
measure  of  the  extent  of  the  spectrum 
produced  by  a  prism. 

The  differences  no—nc  and  np  —  no 
are  partial  dispersions.    The  quotient 

—^ is  represented  by  the  symbol  ^ 

V  and  is  generally  tabulated  in  cata- 
logues of  glass,  as  its  value  is  of  im- 
portance   in   determining   the   desir-  ^'     ^.       '.    T""*^  . 

r  fv  r     ^  Fig.  7.— Dispersion  by  a  prism. 

ability  of  the  different  types  of  glass 

for  use  in  lenses.  While  it  is  universally  represented  by  the  symbol 
V,  no  name  has  been  proposed  which  has  met  with  general  accept- 
ance. The  demand  of  the  instrument  designers  has  led  to  the 
development  by  the  manufacturers  of  a  large  number  of  different 
types  of  glass,  the  optical  constants  of  which  are  tabulated  in  their 
catalogues. 

ATMOSPHERIC    REFRACTION. 

At  a  surface  separating  two  diflerent  media,  the  index  of  refrac- 
tion and  direction  of  a  ray  of  light  changes  abruptly  when  passing 
from  one  side  of  the  surface  to  the  other  in  a  manner  consistent  with 
equation  3.  If  we  have  a  single  medium  in  which  the  index  of  re- 
fraction changes  gradually  as  the  ray  proceeds  from  point  to  point, 
the  course  of  the  ray  will  also  change  gradually  and  will  be  a  curved 
rather  than  a  straight  line.  Accordingly  .the  commonly  made  state- 
ment that  light  travels  in  a  straight  line  is  incorrect  unless  the  path 
is  restricted  to  a  homogeneous  medium.     The  importance  of  this 


14 

lies  in  the  fact  that  the  air  is  ridt  homogeneous,  but  departs  from 
homogeneity  to  such  an  extent  that  the  refraction  arising  therefrom 
must  be  taken  into  account  in  all  precise  levelling  or  operations  of  a 
similar  nature. 

The  index  of  refraction  of  the  air  is  influenced  by  its  density, 
which  varies  with  height,  temperature,  and  amount  of  water  vapor 
present.  The  result  is  that  a  ray  of  light  traveling  through  the  air 
does  not  in  general  follow  a  straight  line  but  is  refracted  and  follows 
a  curved  path. 

For  points  near  the  horizon,  the  bending  is  so  great  that  the  setting 
sun  is  seen  after  it  is  completely  below  the  horizon,  as  determined 
when  atmospheric  refraction  is  ignored.  The  most  important  effect 
of  atmospheric  refraction  is  a  deviation  of  the  ray  in  a  vertical  plane 
which  under  normal  conditions  is  in  such  a  direction  that  an  object 
appears  farther  above  the  horizon  than  it  actually  is.  This  is  illus- 
trated to  an  exaggerated  degree  in  figure  8.  The  arc  CD  represents 
<  the  circumference  of  the  earth.     A 

P  star    in    the    direction   AO    sends 

light  to  the  observer  along  the  path 
EAO.  The  star  actually  appears 
in  the  direction  of  EA'O',  which  is 
the  tangent  drawn  to  the  path  of 
the  light  at  the  point  where  it 
enters    the   eye   of    the   observer. 

FIG.  8.-Refraction  by  the  atmosphere.  ^^    astrOUOmical  WOrk,   COrrCCtionS 

are  applied  to  the  observed  position  of  stars  in  order  to  obtain  the 
true  position. 

If  there  were  no  atmospheric  refraction,  the  distance  L  at  which 
objects  on  the  earth's  surface  could  be  seen  would  be  given  by  the 
equation : 

L=VDH  (7) 


where  D  is  the  diameter  of  the  earth  and  H  the  height  of  the  observer 
above  the  surface  of  the  earth.  If  L  is  measured  in  yards  and  H  in 
feet,  this  equation  becomes: 

L  =  2155VH  (8) 

Atmospheric  refraction  is  based  upon  so  many  factors  that  its 
influence  is  variable.  As  a  first  approximation  it  is  commonly 
assumed  that  when  atmospheric  refraction  is  taken  into  account, 
the  distance  L'  is  given  by  the  equation: 


VI 


DH  (9) 


It  will  be  seen  that  this  is  equivalent  to  the  result  one  would 
obtain  if  there  were  no  atmospheric  refraction  and  the  height  of  the 


15 


observer  were  increased  one-sixth. 
H  in  feet,  the  equation  becomes: 


If  L'  is  measured  in  yards  and 


L'  =  2328VH 


(10) 


On  the  basis  of  these  two  formulre,  atmospheric  refraction  increases 
the  range  of  vision  approximately  8  per  cent.  The  following  table 
shows  the  distance  at  which  an  object  on  the  surface  of  the  earth 
can  be  seen  from  different  elevations.  If  the  object  viewed  is  ele- 
vated above  the  earth's  surface,  it  can  be  seen  at  a  much  greater 
distance.  Accordingly,  additional  columns  are  given  showing  the 
distance  at  which  objects  25  and  50  feet  high  may  be  seen.  These 
values  are  based  upon  the  approximate  refraction  as  embodied  in 
equation  9  and  are  the  limiting  values  for  possible  paths  of  light 
computed  on  this  basis.  The  absorption  of  the  atmosphere  is  not 
taken  into  consideration  and  may  reduce  the  range  of  vision  greatly. 
In  particular,  the  large  ranges  given  at  the  latter  end  of  the  table 
will  be  more  often  realized  over  land  than  over  sea,  due  to  the  greater 
freedom  of  the  atmosphere  from  water  vapor.  Furthermore,  it 
should  be  noted  that  departures  from  the  normal  refraction  on  which 
this  table  is  based  are  not  unusual  and  may  cause  the  geometric 
range  to  differ  greatly  from  the  values  here  tabulated. 


observer, 
in  feet. 

Extreme  distance,  in  yards 

at  which  object  can  be  seen. 

On  surface  of  earth. 

25  feet  above  surface 
of  earth. 

50  feet  above  surface 
of  earth. 

No 
refraction. 

With 
refraction. 

No 
refraction. 

With 
refraction. 

No 
refraction. 

With 
refraction. 

10 
25 
50 
75 
100 

6,800 
10,700 
15,200 
IS,  700 
21,500 

7,400 
11,600 
Ifi,  .500 
20,200 
23,300 

17,  .500 
21,400 
25,900 
29,400 
32,200 

19,000 
23,200 
2s,  100 
31,S0O 
.34,  900 

22,000 
25,900 
30,400 
33,900 
36,700 

23,900 
28,100 
33,000 
36,700 
39,  SOO 

^12.5 
150 
175 
200 

24,100 
2<>,400 
2S,500 
30,500 

26,000 
2S,500 
30,800 
32,900 

34,800 
37,100 
39,200 
41,200 

37, 600 
40, 100 
42,400 
44,500 

39,300 
41,600 
43,700 
45,700 

42,500 
45,000 
47, 300 
49,400 

225 
250 
275 
300 

32,300 
34, 100 
35,  700 
37,300 

34,900 
36,800 
38,600 
40,300 

43, 000 
44,,S00 
46,400 
48,000 

46,  ,500 
4S,  400 
.50,200 
51,900 

47,500 
49,300 
50,900 
52,500 

51,400 
53,300 
.55, 100 
56,800 

325 
350 
375 
400 

as,  800 
40,300 
41,700 
43, 100 

42,000 
43, 600 
45,100 
46,600 

49,500 
51,000 
52,400 
.5.3, 800 

5.3,600 
5.5,200 
56,  7(X) 
5S,  200 

54,000 
5.5,500 
.56,900 
58,300 

,5S,500 
60,100 
61,600 
63,  100 

425 
450 
475 
600 

44,400 
45,  SOO 
47,000 
48,200 

48,000 
49,  400 
50,700 
52,100 

.55, 100 
.56, 500 
57,  700 
O.S900 

59,600 
61,000 

62,  300 

63,  700 

.59,600 
61,000 
62,200 
63,400 

64,  .500 
6,5,900 
67, 200 
6.S,  GOO 

525 
550 
675 
600 

49,400 
50,000 
51,700 
52,800 

53,300 
54,600 
55,800 
57,000 

60,100 
60,  700 
62, 400 
63,  ,500 

64,900 
66,200 
67,400 
6,s,  600 

64,600 
6.5,200 
66,900 
6«,000 

69,  ,S00 
71,100 
72,  ,300 
7.i,  ,500 

625 
650 
675 
700 

53,900 
54,900 
56,000 
57,000 

58,200 
59, 400 
60,500 
61,600 

64,600 

65,  rm 

66,  700 
67,700 

69,  ,SOO 
71,000 

72,  100 

73,  200 

69,100 
70,100 
71,200 
72,200 

74,700 
7.5,  (KX) 
77,000 
7.S,  100 

725 
750 
775 
800 

58,000 
59,000 
60,000 
61,000 

62,700 
63,800 
64,800 
65,800 

6,s,  700 
69,700 
70,700 
71,700 

71,  300 
75,400 
76,400 
77,400 

73,200 
74,200 
75,200 
76,200 

79,  200 

80,  .300 
81,300 
82,300 

IG 

The  depression  position  finder  determines  range  by  measuring  the 
angle  of  depression  of  the  target.  The  atmospheric  refraction  is  so 
great  as  to  make  the  results  entirely  useless  unless  some  compen- 
sating device  is  employed  to  correct  for  the  refraction.  Different 
inventors  have  shown  their  ingenuity  in  effecting  this  correction  by 
various  devices,  and  it  is  here  that  the  fundamental  differences 
between  the  several  types  of  depression  finders  are  found. 

The  bending  of  the  path  of  a  ray  of  light  in  a  horizontal  plane 
is  not  due  to  any  systematic  variation  of  the  refractive  index  and  is 
in  general  so  small  that  it  can  be  neglected  in  readings  taken  with 
fire-control  instruments.  In  very  careful  triangulation  its  effect  is 
eliminated  by  repeating  the  observations  on  different  days  and  under 
different  conditions. 

In  addition  to  the  normal  effects  of  atmospheric  refraction  of  the 
preceding  paragraphs,  anomalous  effects  often  occur.  Over  large 
areas  of  heated  sand  or  over  water,  conditions  are  such  as  to  produce 
strata  of  air  differing  greatly  in  temperature  and  refractive  index. 
This  condition  is  favorable  to  anomalous  atmospheric  refraction 
and  images,  erect  or  inverted,  and  sometimes  much  distorted,  are 
formed  and  can  be  seen  from  a  great  distance.  In  this  manner  at- 
mospheric refraction  gives  rise  to  the  various  forms  of  mirages. 

On  a  hot  day  the  columns  of  heated  air  rising  from  the  earth  are 
optically  different  from  the  surrounding  air  and  a  ray  of  light  is 
irregularly  refracted.  The  air  is  turbulent  and  the  conditions  are 
changing  all  the  time.  Consequently,  an  object  viewed  through 
such  a  layer  of  air  appears  to  be  in  motion  about  a  mean  position. 
In  such  a  case  the  air  is  said  to  be  ''boiling"  or  the  image  is  ''dancing" 
due  to  the  presence  of  "heat  waves."  This  condition  is  particularly 
detrimental  when  a  high-power  telescope  is  employed.  In  fact, 
this  is  such  a  source  of  trouble  that  it  is  usually  impossible  to  use  a 
terrestrial  telescope  of  more  than  twenty  power  with  any  real  benefit. 

With  an  astronomical  telescope,  higher  power  can  in  general  be 
employed  than  with  the  terrestrial  telescope,  as  the  rays  do  not  pass 
through  the  strata  of  dense  air  near  the  surface  so  obliquely  and  the 
greater  portion  of  the  path  of  the  light  is  further  removed  from  the 
surface  of  the  earth. 

PLANE   MIRRORS. 

A  plane  polished  surface  used  to  reflect  light  is  termed  a  "plane 
mirror."  Looking  into  the  mirror  one  sees  objects  which  are  actually 
in  front  of  the  mirror  as  though  they  were  located  back  of  the  re- 
flecting surface.  The  course  of  the  rays  of  light  is  showTi  in  figure  9. 
Suppose  O  is  a  point  sending  forth  rays  of  light.  The  ray  ON  in- 
cident upon  the  mirror  at  N  is  reflected  along  NF,  where  NF  is  so 
drawn  that  the  angle  of  reflection  is  equal  to  the  angle  of  incidence. 
It  may  be  easily  shown  that  NF  will  satisfy  this  condition  if  it  is 


17 


Fig.  9. — Image  of  a  point  ii>  a  plane  mirror. 


drawn  through  N  and  the  point  O'  located  on  the  normal  to  the  mirror 

through  O,  and  as  far  back  of  the  mirror  as  O  is  in  front  of  the  mirror. 

Similarly,    the    ray 

OM    is    reflected 

along  the  line  ME, 

where  ME  produced 

also  passes  through 

O'.     In  fact,  all  rays 

from  O  which   fall 

upon  the  mirror  will, 

after     reflection, 

travel    along    lines 

which    intersect    at 

O'.    Therefore,  if  an 

observer    in     the 

neighborhood  of  E 

or  F  looks  into  the 

mirror,  the  rays  re- 
ceived  by  the   eye 

apparently  proceed 

from    O'    and    the 

point  O  is  seen  in 

the   mirror    appar- 
ently at  O'.     Under  these  conditions  O'  is  said  to  be  the  image  of 

the  object  O.     Such 
A  an   image  is  termed 

' '  virtual ' '  because  the 
rays  do  not  actually 
pass  through  O'  but 
only  appear  to  do  so. 
With  curved  mirrors 
or  lenses  we  shall  have 
examples  of  images 
termed  "real"  in 
which  the  rays  actu- 
ally pass  through  the 
point  where  the  im- 
age is  located. 

If  the  object  before 
the  mirror  is  an  ex- 
tended one,  instead 
of  a  single  luminous 
point,  each  point  will 
have  its  image  back 

of  the  mirror  and  the  ontii'e  object  will  appear  in  true  proportion.     The 

image  will,  however,  be  reversed  in  a  manner  which  is  termed  "  re- 
■18918°— 21 2 


Fir,.  10.— Reversion  by  a  plane  mirror. 


18 

version."  If  we  imagine  the  drawing,  figure  10,  to  represent  a 
plan  view,  the  arrow  viewed  from  a  point  P,  (with  the  mirror  re- 
moved) will  be  seen  with  the  point  to  the  right  of  the  observer.     If 


ABCDE 
FGHI  J 


NORMAL    IMAGE 


3G08^ 
L  I  HOI 


REVERTED  IMAGE 

Fig.  11.— Normal  and  reverted  images. 

the  image  in  the  mirror  is  viewed  from  P,,  the  point  is  to  the  left. 
A  clear  idea  of  reversion  may  be  obtained  by  viewing  the  image  of 
printed  matter  in  a  mirror.  This  is  illustrated  in  figure  11.^  With 
a  single  reflection  the  letters  are  reverted.     If  a  second  mirror  is 


1!) 


employed  so  that  the  image  foimed  by  the  iirst  mirror  is  viewed  in 
the  second,  the  characters  are  reverted  twice  and  are  again  normal. 
In  general,  any  even 
number  of  reflec- 
tions leaves  the  im- 
age in  the  normal, 
any  odd  number  in 
a  reverted  aspect. 

In -figure  12,  the 
method  of  locating 
an  image  formed 
by  two  successive 
reflections  at  two 
mirrors  is  sho^vn. 
The  object  is  at 
O  and  the  image 
formed  by  the  first 
reflection  in  the 
mirror  AB  is  at 
O/.  If  then  we 
consider  0/  as  an 
object  and  locate 
the  image  of  it 
formed  by  the  mir- 
ror CD,  we  obtain 
O,".     This   is    the 


-B 


ima<re  of   O 


V 

-Images  formed  by 

formcd    by 


Fig.  13.— Image  formed  by  two  perpendicular  mirrors. 


wo  successive  reflections. 

two  successive  reflec- 
tions, the  first  of 
which  occurs  at  the 
surface  of  AB.  If 
in  a  similar  man- 
ner we  locate  the' 
image  of  O  in  the 
mirror  CD  and  then 
the  image  of  this 
image  formed  in 
mirror  AB,  we  ob- 
tain the  point  O./', 
which  is  the  image 
of  O,  formed  by 
two  successive  re- 
flections, the  first 
of  which  occurs  in 
tlie  mirror  CD. 
the  two  mirrors,  sees 


The  observer  at  E,  therefore,  on  looking  int 
the  object  at  O  and  the  two  images  0/  and  O,.'  formed  ])y  single  reflec- 


20 


tions.     He  will  also  see  the  two  images  which  are  formed  by  two 

reflections,  one  at  O/'  and  a  second  at  O2".     In  addition  there  will 

be  other  images  visible,  formed  by  more  than  two  reflections  and 

which  are  not  indicated  on  the  drawing.     The  images  formed  by  the 

successively    greater    number    of    reflections    become    progressively 

weaker  as  a  result  of  the  absorption  at  each  reflection  until  they 

finally  become  too  faint  to  be  seen.     But  for  this  limitation,   the 

number  of  images  formed  is  unlimited,  except  in  the  special  cases 

when  the  angle  between  CD  and  AB  is  commensurable  with  360°. 

In  figure  13  such  a  special  case  is  represented  in  which  the  angle 

between  AB  and  CD  is  a  right  angle.     An  eye  at  Ej  sees  the  image 

formed  by  two  reflections,  the  first  in  the  mirror  AB.     An  eye  at 

E2  sees  the  image  in  the  same  position  formed  by  two  reflections,  the 

first  of  which  is  in  the  mirror  CD.     The  coincidence  of  these  two 

images  is  due  to  the  fact  that  90  degrees  has  been  selected  as  the 

angle  between  AB  and  CD.     This  special  case  is  very  important  as 

it  is  the  fundamental  basis  for  the  design  of  all  roof  angle  prisms. 

(See  Prisms.) 

PRISMS. 

In  a  fire-control  instrument  it  is  frequently  desirable  to  bend  the 
rays  of  light  through  an  angle  in  order  to  bring  the  eyepiece  into  a 
more  convenient  position  or  to 
permit  of  a  periscopic  arrangement 
of  parts.  Plane  mirrors  might  be 
employed  for  this,  but  the  silvered 
surfaces  are  a  source  of  trouble,  as 
they  cause  a  loss  of  light  which,  as 
a  result  of  tarnishing,  grows  more 
serious  as  the  instrument  becomes 
older.  Prisms  are  therefore  em- 
ployed for  this  purpose  and  form  a 
very  important  part  of  the  optical 
system  of  an  instrument.  Even 
when  the  relative  location  of  eye- 
piece and  objective  does  not  necessitate  the  use  of  prisms,  they  are,  in 
many  cases,  used  to  erect  an  image  which  would  otherwise  be  inverted. 

The  bending  of  the  rays  by  a  prism  may  be  due  to  refraction,  as 
shown  in  figure  7.  As  shown  in  that  drawing,  however,  it  is  evident 
that  the  rays  of  different  colors  are  bent  through  different  angles.  If 
the  object  to  be  viewed  is  small  and  light  colored,  viewed  through  the 
prism,  it  will  appear  as  an  elongated  streak  made  up  of  spectral  colors. 
When  the  angle  through  which  the  rays  are  bent  is  very  large,  the 
colors  are  so  pronounced  as  to  make  the  use  of  the  prism  impos- 
sible, but  if  the  angle  is  small  a  prism  in  which  the  deviation  is 
wholly  produced  by  refraction  may  be  used.  The  "measuring 
wedge"  in  a  range  finder  (fig.  14)  is  a  prism  of  this  sort.  If  the  inci- 
dent ray  is  normal  to  the  first  surface,  there  is  no  deviation  until  the 


rf^ 

-y 

'r' 

i    / 

~'  ^^~~ 

[f:^A^ 

U. ^Measuring  wodgo  of  range  finder. 


21 


second  surface  is  reached.  If  a  is  the  rofracliu*,'  auj>;le  of  tlie  prism, 
the  angk's  of  incidence  and  refraction  at  the  second  surface  are 
respectively  a  and  r  where  sin  /•  =  ii  sin  a-     Since  the  angles  are  small, 


we  can  assume  the  angles  and  the  sines  identical.     Then, 


(11) 


.Vchromalicpris 


and  the  angle  of  deviation  d  is  given  by  the  equation: 

d  =  na-a={n-  \)a  (12) 

The- total  angle  through  which  the  rays  are  bent  by  the  measuring 
wedge  of  a  range  finder  is  only  a  few  minutes  and  the  separation  of 
the  different  colors  is  so  slight  that 
it  is  not  taken  into  account  in  the 
smaller  range  finders. 

When  the  angle  through  which 
the  rays  are  to  be  bent  is  large,  an 
achromatic  prism  may  be  em- 
ployed. The  construction  is  illus- 
trated in  figure  15.  Two  prisms  are 
cemented  together,  made  of  two 
different  kinds  of  glass.  The  prism 
having  the  smaller  refracting  angle 
is  made  of  heavy  flint  glass  which 
has  a  large  mean  dispersion.  This  prism  is  turned  in  the  opposite 
manner  to  the  first  prism  which  is  of  crown  glass.  The  flint  prism, 
by  reason  of  its  large  dispersion,  neutralizes  the  dispersion  due  to 

the  crown  prism  without  entirely 
neutralizing  the  deviation.  There- 
fore, there  is  a  net  residual  devia- 
tion due  to  the  two  prisms  which  is 
nearly  constant  for  all  colors  and  the 
deviated  image  is  almost  entirely  free 
from  color.  In  some  range  finde-. 
an  achromatic  measuring  wedge  is 
employed  instead  of  the  single  prism 
described  above. 

Even  with  the  achromatic  prism  it 
is  impossible  to  obtain  complete  free- 
dom from  color.  When  reflection 
takes  place  there  is  no  breaking  up  of 
the  ray  into  its  constituent  colors  as  is  the  case  with  refraction.  There- 
fore, the  prisms  used  in  instruments  in  nearly  all  cases  are  of  the  type  in 
which  a  reflecting  surface  is  used  to  produce  the  deviation.  Figure  16 
shows  such  a  prism.  The  ray  indicated  by  the  full  line  falls  upon  the 
first  face  perpendicularly  and  proceeds  as  a  single  ray  without  being 
separated  into  its  component  colors.  At  B  the  angle  of  incidence  is 
such  that  we  have  total  reflection  and  at  th:?  face  HG  the  incidence  is 
again   normal.     Consetiuently    the   ray    traverses    the    entire    prism 


M 

ling  prism. 


22 


without  being  divided  into  its  different  colors.  Tlie  case  is  somewhat 
different  for  a  ray  falling  upon  the  first  surface  obliquely.  The  ray 
shown  by  the  dotted  line  incident  at  J  is  refracted  and  we  should 
expect  to  find  the  final  image  colored.     The  ray,  however,  is  again 


Fig.  17.— Right  angle  reflecting  prism 


Porro  prism. 


refracted  at  L  on  emergence  and  the  two  refractions  are  such  that 
the  one  neutralizes  the  other  and  all  the  parts  of  the  beam,  regardless 
of  color,  are  bent  through  the  same  angle  and  proceed  in  a  common 
direction  after  traversing  the  prism.  The  prism  just  described  is 
known  as  the  right-angle  reflecting  prism  and  is  very  often  used  in 

fire-control  instrn- 
ments  when  it  is  de- 
sired to  bend  the 
rays     through 


an 
angle  of  90°.  Fig- 
ure 17  shows  the 
same  prism  in  per- 
spective. As  there 
is  only  one  reflect- 
ing surface,  the  im- 
age is  reverted. 

The  Porro  prism 
shown  in  figure  18 
is  similar  in  shape 
to  the  right-angle 
prism,  but  the  path 
of  the  rays  is  different.  The  image  is  inverted  in  the  plane  in  which 
reflection  takes  place,  but,  as  there  are  two  reflections,  there  is  no 
reversion.  Two  Porro  prisms  placed  as  shown  in  figure  19  are  used 
in  many  telescopic  systems  to  change  an  inverting  to  an  erecting 
telescope.     It  is  this  system  which  is  commonly  used  in  binoculars. 


XT-I. 

/^^ 

.— ^— -^=== 

-- 

/   ■    '  /^ 

\^<L    1  -""""' 

~~~-~~I2*''"~-^ 

1 

F(G.  1 'J. —Porro  prism  system. 


23 


In  figure  20  there  is  shown  a  second  type  of  Porro  prism  which  is 
often  used  for  securing  an  erect  image.  This  is  substantially  the 
same  in  principle  as  the  first  type.  In  each  case  there  are  four  reflec- 
tions, two  in  each  of  two  planes,  but  the  reflections  occur  in  diflFerent 
order  in  the  two  types. 

The  right-angle  prism  with  roof  is  showTi  in  figure  21.  It  may  be 
considered  as  made  up  of  a  right-angle  reflecting  prism  w^th  the 
hypotenuse  face  replaced  by  two  faces  inclined  to  each  other  at  an 
angle  of  90°.  These  two  faces  form  the  ''roof"  of  the  prism.  The 
lower  prism  of  the  panoramic  sight  and  the  prism  used  in  the  right- 
angle  telescope  of  antiaircraft  fire-control  apparatus  are  of  this  type. 
This  prism  when  inserted  in  a  telescopic  system  bends  the  axis  of  the 
telescope  through  90°  and  also  erects  the  image.  The  course  of  a  ray 
through  the  prism  is  shown  in  the  drawing.  Two  reflections  take 
place,  one  at  each  of  the  two  in- 
clined faces,  and  as  a  result  an 
object  viewed  through  this  prism 


^ 

/,-'"'  \;- 

xy 

—  ^             \^        /y 

Fig.  20.— Second  type  of  Porro  system. 


Fig.  21.— Right  angle  prism  with  roof. 


is  not  reverted.  This  prism  is  one  o'f  the  most  difficult  to  manu- 
facture, as  the  angle  between  the  two  inclined  faces  can  not  differ 
from  90°  by  more  than  a  few  seconds  if  the  prism  is  to  function  satis- 
factorily. The  angle  between  two  such  faces  in  any  prism  is  com- 
monly spoken  of  as  a  "roof  angle"  and  the  same  high  degree  of 
accuracy  in  its  construction  is  always  demanded.  If  the  angle  is 
not  accurately  made,  the  image  in  the  center  of  the  field  will  appear 
doubled  and  the  prism  is  entirely  useless.  This  doubling  arises  from 
the  fact  that  a  portion  of  the  rays  are  incident  upon  the  two  faces 
in  one  order,  the  remainder  in  the  reverse  order.  The  images  by  the 
two  portions  do  not  coincide.  If  the  angle  is  precisely  90°,  the  images 
produced  by  the  two  reflections,  regardless  of  the  order  in  which 
the  reflections  occur,  coincide,  as  shown  in  figure  13.  The  doubling 
of  images  then  disappears.     Angles  having  the  requisite  accuracy  can 


24 


not  be  produced  directly,  but  must  first  be  carefully  approximated 
by  usual  manufacturing  methods  after  which  the  faces  must  be  care 
fully  ground  by  a  skilled  operator  and  individually 
tested  until  the  angle  is  so  nearly  correct  that  the 
image  is  not  doubled.  An  error  of  a  few  seconds  is 
sufficient  to  make  the  prism  worthless.  This 
tedious  method  of  production  limits  the  output,  as 
few  men  become  sufficiently  skilled  to  do  this 
local  retouching. 

In  the  rotating  prism  shown  in  figure  22  the  light 
undergoes  a  single  reflection,  after  which  it  contin- 
ues in  its  original  direction.  The  image  is  reverted 
by  the  single  reflection.  It  is  by  means  of  this 
prism  that  the  image  in  the  panoramic  sight  is 
caused  to  remain  erect  as  the  upper  head  is  rotated 
in  azimuth. 

The  Brashear-Hastings  prism  (figure  23)  is  a 
type  of  erecting  prism  in  which  there  is  no  dis- 
placement of  the  ray.  Four  reflections  take  place, 
two  at  the  upper  sloping  faces  and  two  at  the  lower 
pair  of  faces,  which  are  inclined  to  each  other  at 
an  angle  of  90°  and  which  form  a  roof.  This  prism 
is  subject  to  the  same  difficulty  in  production  as 
the  roof  angle  prism,  previously  described,  as  the 
angle  between  the  two  lower  faces  must  be  accu- 
rately 90°. 

In  figure   24   there  is  shown   another  type  of 

erecting  prism  which  is  used  more  frequently  by 

Em-opean  than  by  American  manufacturers.     The 

Fig.  22.-Rotating  prism,     advantages 'of  this  prism  are  that  it  can  be  made 


^i. 


t     =. 

p? 

>    -M 

U' 

V 

^ 

— 1 

\y     ,  ••?-/         yi^ 

Fig.  23.— Brashear-Hastings  erecting  prism. 

in  one  piece  and  is  of  such  shape  that  it  can  be  held  very  rigidly  in 
an  instrument.  The  last  two  reflecting  surfaces  form  a  roof  angle. 
This  is  designated  as  the  Sprenger  prism. 


25 


The  erecting  prism  used  in  (he  Amei;ican  aiming  circle,  model  1916, 
is  shown  in  figure 
25.  This  design  of 
erecting  prism  is 
only  used  in  aiming 
circles  of  this  type 
where  itlends itself 
to  the  design  of  a 
compact  instru- 
ment. Inthedraw- 
ing  only  three  re- 
flections are  indi- 
cated and  theimage 
will  be  reverted,  as 
an  odd  number  of 
reflections  always 
implies  a  reverted 
image.  This  erect- 
ing prism  is  used 
with  a  right  angle 
reflecting  prism 
which  is  inserted  in 
the  optical  train  at 
a  different  point. 


^^^^^^"^-^ 

M 

^+ 

Vks) 

Fig.  24.— Sprenger  erecting  prism. 


The  four  reflection,^; 


an  erect  image.  The 
second  reflection 
indicated  in  figure 
25  occurs  at  an  an- 
gle of  incidence  less 
than  the  critical  an- 
gle, and  the  surface 
at  which  this  reflec- 
tion takes  place  is 
therefore  silvered. 

The  triple  mirror 
shown  in  figure  2G 
has  three  reflecting 
facts  which  are  mu- 
tually orthogonal. 
It  has  the  peculiar 
property  of  deviat- 
ing any  ray  which 
enters  it  through 
an  angle  of  180°— 
,.„  o-    TT    .■        .       ,  •  •      ■  ,  that  is,  the  ray  is 

Jir..  2i.— Erecting  system  of  aiming  circle.  ^ 

returned    along    a 
course  parallel  to  its  original   path  and  in  the  opposite  direction. 


26 


If  11 


angles  are  accurately  made,  this  parallelism  is  true,  no  matter 
how  the  prism  is  turned  so  long  as 
it  receives  the  incident  light.  Use 
is  made  of  this  prism  in  signalling 
devices  and  in  the  internal  adjust- 
ment device  of  small  range  finders. 
The  penta  prism  illustrated  in  fig- 
ure 27  is  used  in  the  range  finder  as 
an  end  reflecting  prism.  The  devi- 
ation of  the  ray,  which  is  90°,  is 
independent  of  any  small  rotation 
of  the  prism  in  the  plane  of  reflec- 
tion. The  fact  that  the  deviation 
Fir..  2o.-Tripie  mirror.  ^^   coustaut    is  the   feature  which 


makes  this  prism 
useful  in  range  fin- 
ders. The  angles 
measured  by  the 
range  finder  are  so 
small  that  if  a  con- 
stant deviation 
prism  were  not 
used  the  variation 
in  the  angles  of  de- 
viation at  the  end 
reflectors  brought 
about  by  the  flex- 
ure of  the  tube  and 
consequent     rota- 


/        1       / 

/  J?"'^ 

\ 

'  1 

1     ^> 

k 

Fir..  2S.— Rhomboidal  prism. 

fore  substituted.     Two  silvered 


Fin.  27.  — Ppnla  prism. 

tion  of  the  prisms  would  be  suffi- 
cient to  impair  the  accuracy  of  the 
range  finder.  1 1  is  necessary  to  sil- 
ver the  reflecting  surfaces  of  the 
penta  prism,  as  the  rays  fall  upon 
the  reflecting  surfaces  at  angles  less 
than  the  critical  angle.  We  there- 
fore do  not  have  total  reflection. 

In  the  very  long  base  range 
finder  the  penta  prisms  are  so  large 
that  it  is  diflicult  to  find  a  block  of 
glass  sufficiently  large  and  homo- 
geneous for  the  construction  of  a 
prism.  Penta  reflectors  are  there- 
3-lass  mirrors  are  held  in  a  metal 


27 


frame  in  such  a  way  that  they  occupy  positions  analogous  to  the  two 
reflecting  surfaces  of  the  prism.  It  is  necessary  that  the  mirrors  be 
held  rigidly  and  permanently  in  the  desired  positions  and  that  temper- 
ature changes,  so  far  as  possible,  be  eliminated. 

Figure  28  illustrates  the  rhomboidal  prism.  This  may  be  con- 
sidered as  made  up  of  two  right  angle  reflecting  prisms  built  in  one 
piece.  It  does  not  invert  or  revert  the  image  nor  change  the  direc- 
tion of  the  beam  of  light  but  displaces  it  parallel  to  itself.  This 
prism  forms  one  of  the  components  of  the  ocular  prism  of  the  range 
finder  and  is  also  used  in  one  of  the  systems  for  internal  adjustment. 

THE  SPHERICAL  REFLECTING  SURFACE. 

In  figure  29  the  arc  passing  through  V  with  center  at  C  represents 
the  trace  of  a  concave  spherical  reflecting  surface.     The  line  OV  is 


.  Fig.  29.— Reflection  at  a  spherical  surface. 

termed  the  ''  axis  "  of  the  mirror  and  the  point  V,  the  "  vertex."  The 
location  of  the  image  of  the  point  O  is  to  be  determined.  A  ray  from 
O  incident  upon  the  mirror  at  I  is  reflected  in  the  direction  10', 
where  10'  is  so  drawn  that  angle  OIC  equals  angle  O'IC. 

The  following  sign  convention  is  to  be  adopted:  The  length  of  a 
line  generated  by  a  point  starting  at  V  and  moving  in  the  direction 
of  the  incident  light  is  positive.  Lengths  extending  in  the  opposite 
sense  are  negative. 


28 

In  accordanco  with  this  statement 

VO,  which  will  be  represented  by  u,  is  negative. 
VO',  which  will  be  represented  by  u' ,  is  negative. 
VC,  which  will  be  represented  by  r,  is  negative. 

This  convention  which  in  the  present  case  makes  all  lengths  nega- 
tive has  been  adopted  in  order  that  a  generalization  may  be  made, 
including  the  equations  for  both  reflecting  and  refracting  surfaces. 

In  triandes  OIC  and  O'lC 


u  —  r    sm  ^ 
r    ~"sin  I 

(13) 

r  —  u'     sin  i' 

(14) 

r        sin  V 

Since  the  angles  of  incidence  and  reflection  are  equal, 

sin  i  =  sin  i' 

(15) 

Combining  these  equations,  then, 

u~r     sin  Z' 
r  —  u'     sin  Z 

(16) 

r  —  u       sm 

r 

If  I  is  near  V  and  consequently  angles 

I  and  V 

are 

small, 

we  may 

make  the  approximation: 

sin  /  =  — 
u 

h 

(17) 

sin?'=-^p 

Equation  16  then  becomes 

u  —  r          u 
r-u~^u' 

which  may  be  written 

1      1  _ 

u     u' 

2 
r 

(18) 

The  focal  length,  which  will  be  denoted  by/,  is  equal  to  the  recip- 
rocal of  the  right  hand  member  of  equation  14. 

It  should  be  noted  that  in  the  case  here  selected  /"  is  positive, 
although  the  negative  sign  appears  explicitly  in  the  equation.  This 
arises  from  the  fact  that  with  the  convention  of  signs  which  has 
been  adopted  r  is  negative.     Equation  14  may  be  written, 

_1-Vi  (20) 

u    u'    f 


29 


-Parallel  rays  projected  by 
mirror. 


The  approximations  which  were  made  in  equation  17  have  a  simple 
physical  interpretation.  A  ray  from  O,  incident  upon  the  mirror  at 
I,  cuts  the  axis  OV  at  a  point  near 
O'.  If  I  is  considered  as  a  variable 
point  approaching  V  as  a  limit,  then 
this  point  is  also  variable  and  ap- 
proaches as  a  limit  the  point  O'  lo- 
cated by  equation  19  or  20.  The  rays 
from  O,  incident  upon  the  mirror,  af- 
ter reflection,  do  not  all  pass  through 
a  single  point,  but  if  IV  is  not  too 
large  they  do  pass  very  near  to  the 
point  O'.  Therefore  O'  is  the  image  of  O,  although  there  is  not  the  per- 
fect concurrence  of  the  rays  after  reflection  as  with  the  plane  mirror. 

The  rays  after  reflection  from 
the  plane  mirror  did  not  actually 
pass  through  the  image  but  only 
appeared  to  proceed  from  a  com- 
mon point.  The  image  was  said  to 
be  virtual.  In  the  present  case 
the  rays  actually  pass  through  O' 
(to  the  degree  of  approximation 
indicated  above)  and  the  image  is 
accordingly  real. 

In  equation  20,  if  u  increases 
indefinitely,  u'  approaches  —/as  a 
limit.  As  u  increases,  the  rays  fall- 
ing upon  the  mirror  become  more 
nearly  parallel.  If  the  rays  are 
strictly  parallel,  we  have  the  lim- 
iting condition  and  the  image  is  at 
O',  figure  30,  where  VO'  equals  /. 
The  focal  length  may  therefore  be 
defined  as  the  distance  from  the 
vertex  of  the  mirror  to  the  image 
formed  of  an  object  at  an  infinite 
distance. 

Conversely,  if  the  point  O  ap- 
proaches the  mirror,  u'  increases 
and  becomes  infinite  when  u  equals 
-/.  A  source  at  O',  figure  30,  then 
sends  forth  rays  which,  after  re- 
flection, are  parallel.  It  should  be 
observed  tliat  tlie  paraUelism  of  rays  here  referred  to  is  only  ap- 
proximate and  is  conditioned  upon  the  as.sumption  introduced  in  the 
derivation  of  equation  17,  i.  e.,  that  IV  is  small. 


Fig.  31.— Projection  by  a  spherical  and  parabolic 
mirror. 


30 

If  we  wish  to  illuminate  a  distant  object,  it  is  advantageous  to 
place  the  source  at  the  focus  of  a  concave  mirror,  as  sho^\^l  in  figure 
30.  All  the  rays  which  fall  upon  the  mirror  are  then  projected  in 
a  common  direction  and  fall  upon  the  distant  point.  It  is  further- 
more seen  that  it  is  advantageous  to  make  the  mirror  as  large  as 
possible  in  order  that  it  will  receive  a  greater  proportion  of  the  rays 
from  the  source  and  hence  concentrate  more  light  upon  the  distant 
object.  But  as  the  mirror  is  made  larger,  the  assumptions  of  equa- 
tion 1 7  become  more  and  more  inaccurate  and  the  parallelism  of  .the 
projected  rays  becomes  less  perfect.  If,  instead  of  the  spherical 
surface,  the  mirror  is  made  a  paraboloid  of  revolution  and  the  source 
placed  at  the  focus,  the  geometrical  properties  of  such  a  surface  are 
such  that  all  the  rays  are  projected  in  a  parallel  beam,  no  matter  how 
large  a  portion  of  the  surface  is  utilized.  Figure  31  shows  on  an 
exaggerated  scale  the  difference  in  the  action  of  the  spherical  and 
parabolic  reflector. 

In  the  drawing  it  appears  as  though  the  rays  from  the  spherical 
mirror  converged  and  that  this  form  might  be  the  more  favorable. 
The  converging  rays,  however,  cross  at  a  point  relatively  near  the 
searclilight,  after  which  they  diverge,  so  the  net  result  in  an  actual 
application  is  a  divergence.  The  fundamental  parts  of  the  search- 
light are  a  brilliant  small  source  of  light  and  a  paraboloid  reflector. 

THE  SPHERICAL  REFRACTING  SURFACE. 

The  arc  AB  (fig.  32)  is  a  curved  refracting  surface  with  center  at 
C  and  vertex  at  V.  The  object  is  at  O  and  the  course  of  a  ray  is 
represented  which  is  incident  upon  the  lens  at  I  and,  after  refraction, 
passes  through  the  image  point  at  O'. 

If  the  same  sign  convention  adopted  for  the  reflecting  surface  is 
used, 

VO,  which  will  be  represented  by  u,  is  negative. 

VO',  which  will  be  represented  by  u',  is  positive. 
VC,  which  will  be  represented  by  r,  is  positive. 

In  the  triangle  OIC 

OC     —u  +  r        sin  i 


IC  r  sin  I 

Similarly  in  triangle  O'lC, 


(21) 


CO'     -r+ri'^_^su^^  ^^2) 


IC  r       ~  ^sin  I 

Combining  these  two  equations 


-u+r      ^sini^'  (23) 


—  r+u'        sin  i'  sin  I 


31 


Since,  in  accordance  witli  tlio  law  of  refraction '  •     ^,  =    -  this  may  be 
'  sin  in,  -^ 


written 


■  li  +  /• 

■r  +u' 


n,  sin  I 


(24) 


Now  if,  as  in  the  case  of  tlie  sj)lieri(»il  reflectin<i^  surface,  we  assume 
that  I  api)roaches  V  as  a  limit,  "^.     ,  ajjproaches  as  a  limit  the  value 


Substitutinj 


u  +  r 
r+u' 


n.,u 


(25) 


Fig.  32.— Refraction  at  a  spherical  surface. 


and  this  may  be  A\Titten : 


77,     na^ri;- 
u      u'         r 


(26) 


As  in  the  case  of  the  curved  mirror,  the  image  at  O'  is  ap{)roximate 
and  the  approximation  improves  as  IV  is  made  smaller. 

It  will  be  noted  that  if  n,  =  1,  713=  —  1,  equations  26  and  18  become 
identical.  In  general  the  equations  for  reflecting  surfaces  can  be 
obtained  directly  from  the  corresponding  equations  for  refracting 
surfaces  by  making:  the  above  substitution. 


THE   THIN    LENS. 

In  the  elementary  development  of  formuhe  for  the  action  of  a  lens 
it  is  usual  to  assume  that  the  thickness  of  the  lens  may  be  neglected. 
This  results  in  a  great  simplification  of  the  formuhe  and  the  approxi- 
mation is  sufficiently  accurate  to  be  useful,  as  in  a  large  number  of 
lenses  the  thickness  is  very  small  in  comparison  with  the  other  lengths 


32 

which  are  involved.  Formulae  in  which  this  assumption  is  made  are 
referred  to  as  "thin  lens  formulae." 

A  lens  consists  essentially  of  two  refracting  surfaces  which  act 
successively  upon  the  light,  and  by  applying  formula  26  for  the  single 
refracting  surface  twice  we  obtain  the  resultant  effect  of  the  lens. 

In  figure  33  the  lens  is  bounded  by  the  two  spherical  surfaces 
having  vertices  at  Vi  and  V2.  The  image  formed  by  the  first  surface 
is  at  0\.  Let  VjO  and  ViO'i  equal  u  and  u\,  respectively.  Then 
for  r?!  and  %  of  formula  26  substitute  1,  the  index  of  air,  and  n,-  the 
index  of  the  material  of  the  lens.     The  equation  becomes 

_i+iL_'l^  (27) 

_L=r!iiLi+ni  (28) 

The  image  formed  by  the  first  surface  is  to  be  considered  as  the 


object  for  the  second  surface  and  the  final  image  produced  by  the 
lens  located.  The  distance  from  the  second  surface  to  the  object 
is  V20'i,  but  since  the  thickness  is  to  be  neglected  this  is  the  same 
as  VjO',  which  has  already  been  determined.  A  second  application 
of  formula  26  with  iiy  and  %  replaced,  respectively,  by  n  and  1  gives 

_r!izii+n+L,=i^  (29) 

Transposing 

-!  +  7'  =  (^-l)R-n  (30) 

In  this  formula  the  sign  convention  previously  laid  dov^m  is  to  be 
followed,  i.  e.,  w  and  u'  are  to  be  measured  from  the  lens  to  the  ob- 
ject and  image,  respectively,  and  the  length  is  positive  if  it  extends  in 
the  direction  of  the  incident  light.  In  figure  33,  u  is  negative  and  u' 
is  positive. 

Radii  of  curvature  are  positive  when  convex  toward  the  incident 
light.     In  figure  33,  r^  is  positive  and  r.,  is  negative. 


33 


If  wc  write 


equation  30  l)ecomcs 


f< 


«-'{'^] 


u     u 


(31) 


(32) 


The  value  of /has  the  same  significance  as  with  the  reflecting  sur- 
face. If  parallel  rays  fall  upon  the  lens,  u  is  infinite  and  u'  equals/, 
i.  e.,.the  rays  pass  through  a  point 
ilistant/from  the  lens.  If  a  source 
of  light  is  placed  at  this  point, 
the  rays  which  are  intercepted  hy 
the  lens  are  projected  as  a  par- 
allel beam.  This  explains  the  use 
of  the  "bull's-eye"  lens  to  project 
the  beam  of  light  from  a  flash 
lamp.  For  a  searclilight  the  lens 
is  not  so  adaptable  as  the  mirror, 
as  the  lens  would  require  for  its  construction  glass  of  a  homogeneity 
difficult  to  secure  and  the  thickness  at  the  center  would  be  so  great 
that  the  lens  would  absorb  a  large  part  of  the  light. 


Divergent  lens. 


DOUBLE  CONVEX.  PLANO  CONVEX.  MENISCUS  CONVERGING. 

CONVERGING. 


DOUBLE    CONCAVE.      PLANO    CONCAVE.      MENISCUS     DIVERGING. 


DIVERGING. 

Fig.  :i5.— Types  of  len.^es. 

A  thin  lens  of  the  form  shown  in  figure  33  renders  a  pencil  of  light 
falHng  upon  it  more  convergent.     A  convergent  lens,  often  called  a 
positive  lens,  is  characterizecl  by  the  fact  that  it  is  thicker  in  the  ccn- 
48918°— 21 ?, 


ter  than  at  the  edge  and  has  a  positive  focal  length  as  defined  by 
equation  31.  Figure  34  illustrates  a  divergent  or  negative  lens 
which  is  always  tliinner  at  the  center  than  at  the  edge.  A  pencil  of 
light  diverging  from  the  point  O  is  rendered  more  divergent  by  the 
lens  and  apparently  proceeds  from  O',  which  is  a  virtual  image.    The 

classification  of  con-r 
verging  and  diverg- 
ing lenses  based 
upon  their  shape  is 
illustrated  in  figure 
35.  Figure  36  illus- 
trates the  action  of  a 
converging  and  di- 
verging lens,  respec- 
tively, upon  a  par- 
allel beam  of  light. 
In  the  first  case  a 
real  image  is  formed 
distant  /  from  the 
lens.  In  the  second 
case  the  image  is  vir- 
tual, distant /from 
the  lens  and  on  the 
side    as    the 


same 


3rgent  and  divergent  leu.ses 


source. 

Thus  far  only  the 
images  of  points  ly- 
ing on  the  optical 
axis  of  the  lens  have 
been  considered.  In  figure  37  let  the  arrow  OOi  represent  an 
extended  object.  The  image  of  O  is  at  O'.  To  locate  the  image 
of  0„  consider  the  path  of  the  ray  OjC.  If  the  thickness  of  the  lens 
is  neglected  this  ray  will  be  equally  refracted  at  the  two  coincident 
surfaces  and  will  be 

a ^  ^    ^ 


undeviated.  It  may 
therefore  be  ex- 
tended as  a  straight 
line.  The  ray  OJ., 
which  is  parallel  to 
the  axis  of  the  lens, 
will  after  refraction 
pass  through  F,  the  focus  of  the  lens.  Since  the  intersection 
of  any  two  rays  serves  to  locate  the  image,  0/  is  the  image 
of  Oi.  These  two  particular  rays  were  selected  because  theu" 
courses  after  refraction  could  be  easily  determined.  The  image 
O'O/  is  inverted  and  in  general  will  differ  in  size  from  the  object. 


Fig.  37.— Image  of  an  extended  object  by  a  thin  leii 


35 


(33) 


If  y  aiul  y'  are  the  length  of  ima<;e  and  object,  respectively, 

y     OiO,       u 

This  equation  gives  the  magnification  of  the  object.  In  the  case 
represented  in  figure  37,  '/  is  negative  and  u'  positive.  The  quotient 
is  negative  and  tliis  is  to  be  interpreted  as  denoting  that  the  image  is 
inverted.  , 

Figure  38  illus-     Q 
trates  the  relation-     '[^^"^-'^v-^ 
ship  of  object  and      1  ^^^:^--.^ 


a 


--Q---- 


Fig.  3S.— Magnification  prcxluced  by  a  positive  lens. 


image,  for  a  con- 
verging lens  when 
the  image  is  vir- 
tual. The  image 
of  the  arrow  is 
much  enlarged, 
erect  and  oii  the 
same  side  of  the  lens  as  the  object.  This  illustrates  the  action  of  the 
simple  magnifying  lens  or  reading  glass. 

The  image  formed  by  a  diverging  lens  is  illustrated  in  figure  39. 
For  the  case  here  selected  the  image  is  virtual  erect  and  much  smaller 
than  the  object.  Under  these  conditions,  then,  a  diverging  lens  does 
not  magnify  an  object  but  makes  it  appear  smaller.  The  lens  placed  in 
the  floor  of  an  airplane  for  observation  operates  upon  this  principle.  It 
makes  objects  appear  smaller  than  when  viewed  with  the  unaided  eye 
but  has  a  compensating  advantage  in  that  the  field  of  view  which 

may  be  observed  through  the  rela- 
tively small  opening  is  much  larger 
than  would  be  possible  if  the  lens 
were  not  used. 

The  lenses  treated  above  have  had 
only  spherical  or  plane  refracting  sur- 
faces. Spectacle  lenses  having  one 
surface  cylindrical  instead  of  spher- 
ical are  commonly  employed  in  order 
to  correct  the  eye  for  astigmatism.  The  action  of  such  lenses  is 
illustrated  in  figure  40.  In  planes  passing  through  the  object  point 
O  and  parallel  to  the  elements  of  the  cylindrical  surface,  as  indi- 
cated by  the  shading  of  the  drawing,  there  is  no  converging  or 
diverging  effect.  In  planes  perpendicular  to  these  first  mentioned 
planes  and  passing  through  O,  the  rays  are  caused  to  converge  or 
diverge,  accordingly  as  the  lens  is  thicker  or  thinner  in  the  center 
than  at  the  edge. 


Fig.  39.— KediKtioii  produced  by  a  negative 


36 


The  upper  drtu\dng  illustrates  a  converging  cylindrical  lens.  The 
ray  01  which  passes  symmetrically  through  the  cylindrical  lens  is 
undeviated.  A  plane  pencil  of  rays,  as  represented  by  rays  OA, 
OB,  and  OC  remains  in  the  original  plane  but  is  caused  to  converge 
and  is  brought  to  a  focus  at  the  point  I,.  The  symmetrically  sit- 
uated plane  pencil  is  brought  to  a  focus  at  I.,.  Intermediate  plane 
pencils  are  brought  to  a  focus  at  intermediate  points  and  the  final 
result  is  that  all  rays  proceeding  from  the  point  O  which  are  re- 
fracted by  the  lens  pass  through  the  line  1,  h.  This  line  is  there- 
fore a  real  image  of  the  point  O. 

If  the  refracted  rays  are  produced  backward  through  the  lens, 
they  are  seen  to  pass  through  the  line  I3  I^.  This  line  is  therefore 
a  virtual  image  of  the  point  O. 

The  cylindrical  lens  therefore  forms  two  images  of  the  point  O, 
each  of  which  is  a  straight  line.  Furthermore,  it  is  easily  seen  that 
the  two  lines  are  perpendicular  to  each  other  and  intersect  the  line 


OX 


Fig.  40.— Action  of  eylindrical  lens. 


01  at  right  angles.  In  general,  a  cylindrical  lens  forms  two  such 
images  of  a  point  and  as  the  position  of  the  object  or  type  of  lens  is 
changed,  they  may  be  both  real,  both  virtual,  or  one  real  and  one 
virtual,  as  in  the  illustrated  case.  In  the  last  two  drawings  the 
action  of  a  diverging  cylindrical  lens  is  illustrated.  In  this  case 
both  images  are  virtual. 

When  a  point  is  imaged  as  two  perpendicular  straight  lines,  the 
image  is  said  to  be  astigmatic.  A  further  treatment  of  such  images 
is  given  in  connection  with  the  aberration  of  a  lens. 

In  the  large  horizontal  base  range  finders  two  cylindrical  lenses 
are  mounted  so  that  they  may  be  swung  into  the  path  of  the  light. 
They  are  termed  "  astigmatizers "  and  are  employed  when  ranges 
are  to  be  read  and  the  only  target  offered  is  a  searchlight.  Without 
the  cylindrical  lenses  the  searclilight  appears  as  a  small  bright  spot 
and  it  is  difficult  to  keep  it  upon  the  dividing  line  in  the  range  finder. 
When  the  cjdindrical  lenses  are  in  position  the  image  of  the  search- 


37 

liglit  is  drawn  out  into  a  luminous  lino  perpendicular  to  tlie  dividing 
line  and  the  readin*!;  of  the  ran<jje  is  niucii  facilitated. 

THICK    LENSES   AND    COMBINATIONS. 

For  many  purposes  the  approximate  formulae  already  given  are 
sufficiently  accurate.  So  long  as  the  thickness  of  the  lens  is  negligihle, 
it  is  a  matter  of  indifference  from  what  portion  of  the  lens,  center  or 
surface,  the  distances  u  and  v  are  measured.  When  the  thickness 
of  the  lens  is  too  great  to  be  ignored,  equation  32  will  still  be  true  if  u 
and  u'  are  measured  from  the  two  principal  points  and  if  for  /' we 
write  the  equivalent  focal  length. 

The  two  principal  points  lie  on  the  axis  of  the  lens  and  are  conjugate; 
that  is,  one  point  is  the  image  of  the  other.  Therefore  any  incident 
ray  which  passes  through  the  first  point  has  a  corresponding  emergent 
ray  which  passes  through  the  second  point.     Furthermore,  two  such 


rays  make  equal  angles  with  the  optic  axis.  For  this  reason  these 
two  points  are  sometimes  called  points  of  unit  angular  magnification. 
The  principal  ])oints  are  shown  in  figure  41  at  P,  and  P... 

The  locations  of  the  two  principal  points  are  given  by 
tions : 

V  P  ^^' 

*  1-^  1 


n{r. 


V..P, 


t{n-\) 


tlie  e([ua- 
(34) 


(35) 


n{j\  —  To)  —  <(n—  1) 

Tlie  thickness  of  the  lens  is  /  and  the  distances,  when  measured  in 
the  sense  indicated,  are  j)()sitive  if  they  extend  in  the  direction  of  the 
incident  light. 

For  a  double  convex  or  concave  lens  the  two  principal  points  are  in 
the  lens  and,  if  the  two  surfaces  are  equally  curved,  are  equidistant 


from  the  two  surfaces.  If  one  surface  is  more  strongly  curved  than 
the  other,  both  points  tend  to  move  toward  the  more  curved  surface. 
If  one  surface  of  the  lens  is  plane,  one  principal  point  lies  at  the  vertex 
of  the  curved  surface.  If  the  lens  is  meniscus,  one  or  both  points  will 
lie  outside  the  lens. 

A  tliick  lens  has  three  focal  lengths,  the  equivalent  focal  length 
(E.  F.  L.)  the  back  focal  length  (B.  F.  L.),  and  the  front  focal  length 
(F.  F.  L.).  The  equivalent  focal  length  is  the  focal  length  of  a 
"thin"  lens  which  will  form  an  image  the  same  size  as  that  formed 
by  the  thick  lens  provided  that  the  distance  from  object  to  thin  lens 
equals  the  distance  from  object  to  first  principal  point  of  thick  lens. 
The  value  of  the  equivalent  focal  length  is  given  by  the  formula : 


E.  F.  L. 


in-l)[n{r,-r,)+t{n-l)] 


(36) 


Fig.  42.— Method  of  locating  the  image  formed  by  a  thick  lens. 


In  figure  41  the  principal  points  are  shown  at  P^  and  F^.     Parallel 

rays  from  the  left 
are  brought  to  a 
focus  at  Fj,  similar 
rays  from  the  right 
at  ¥,. 

The  distance  P^Fj 
or  PjFi  is  the  equiv- 
alent focal  length. 
The  back  focal 
length  is  VaF,,  i.  e., 
it  is  measured  from 
the  vertex  of  the 
lens  instead  of  the  principal  point.  The  corresponding  distance  ViFi  is 
the  front  focal  length.  These  last  two  focal  lengths  may  be  found 
■by  equations  34,  35,  and  36.  The  equivalent  focal  lengths  on  the 
two  sides  of  the  lens  are  equal  but  the  back  focal  length  and  front 
focal  length  are  equal  only  when  ViPi  equals  P.Vj  which  is  only  true 
for  a  symmetrical  lens. 

Two  planes  passing  through  the  two  principal  points  and  perpen- 
dicular to  the  axis  of  the  lens  are  termed  the  two  principal  planes. 
These  are  sometimes  referred  to  as  the  planes  of  unit  magnification, 
as  a  ray  incident  upon  the  lens  falls  upon  the  first  principal  plane  at 
the  same  distance  from  the  axis  as  the  conjugate  emergent  ray  inter- 
sects the  second.  This  fact,  together  with  the  unit  angular  magnifica- 
tion at  the  principal  points,  enables  one  to  easily  determine  graphically 
the  position  of  the  image  of  any  point  not  on  the  axis  of  the  lens.  Let 
O  in  figure  42  be  the  point  in  question,  APi  and  A'Pj  the  principal 
planes,  and  Pj  and  P,  the  principal  points.  The  lens  itself  is  not 
shown,  as  the  principal  planes  and  equivalent  focal  length  P^F  define 


39 

all  its  properties.  The  ray  OPi  will  emerge  at  P,  and  the  entrant  and 
emergent  rays  make  equal  angles  with  the  axis  of  the  lens.  This 
enables  P.O'  to  be  drawn.  The  ray  OA  is  parallel  to  the  axis  of  the 
lens.  The  conjugate  ray  must  be  drawn  through  A'  (APi  =  A'P2) 
and  will  pass  through  F.  The  intersection  at  O'  is  the  image  of  O.- 
The  conjugate  ray  to  any  ray  OB  can  now  be  easily  dra\\Ti.  It  passes 
through  points  B'  and  O'. 

To  determine  the  location  of  the  image  of  an  axial  point,  equation 
32  mray  be  used.  The  distances  u  and  v'  are  measured  from  the  prin- 
cipal points,  and  for/  the  equivalent  focal  length  is  to  be  used. 

If  two  thin  lenses  of  focal  lengths,/  and/,  are  placed  in  contact, 
the  focal  length  of  the  resulting  system  is  given  by  the  equation: 

^Vlien  the  lenses  are  thick  lenses  or  are  not  in  contact,  the  equivalent 
focal  length  of  the  system  is  given  by  the  equation: 

In  this  equation /i  and/,  are  the  equivalent  focal  lengths  of  the  two 
component  lenses  and  ,s  is  the  distance  from  the  second  principal 
point  of  the  fu-st  lens  to  the  first  principal  point  of  the  second  lens. 
The  usual  sign  convention  holds  for  s  and  the  measurement  is  to  be 
made  in  tiie  direction  indicated.  It  should  be  noted  that  when  the 
two  lenses  are  in  actual  contact,  as  the  two  components  of  a  cemented 
objective,  -s  in  general  is  not  zero,  as  the  distance  is  measured  between 
the  two  principal  points  and  not  between  the  two  surfaces. 

The  system  of  two  lenses  may  be  considered  as  equivalent  to  a  thick 
lens  having  an  equivalent  focal  length  given  by  equation  38  and  two 
principal  points  given  by  the  equations : 

P.f.  =  y7^|'r:,  (39) 

The  distances  p^Pi  is  measured  from  the  first  principal  point  of 
the  first  component  lens  to  the  principal  point  of  the  equivalent  thick 
lens,  the  distance  p.P,  from  the  second  principal  point  of  the  second 
lens  to  the  second  principal  point  of  the  equivalent  lens. 

If  the  ef[uivalent  single  tliick  lens  is  to  be  determined  corresponding 
to  three  or  more  component  lenses,  two  may  first  be  combined  by  the 
preceding  equations.  The  equivalent  lens  thus  obtained  may  then 
be  combined  with  a  third  and  the  process  continued  successively 
until  all  are  combined. 


Z-L  ^^^^==5^ 

/  "~*    ^~^^^ 

/___,--— -;^ 

40 

THE   ABERRATIONS   OF  A   LENS. 

In  determining  the  location  of  the  image  formed  by  a  lens,  certain 
approximations  have  been  made  in  the  mathematical  equations. 
It  has  been  assumed  that  the  angles  dealt  with  were  so  small  that 
•angles,  sines,  and  tangents  could  all  be  considered  equal.  This  is 
equivalent  to  assuming  that  the  only  rays  which  form  the  image  are 
those  traveling  in  a  direction  nearly  parallel  to  the  axis  of  the  lens 
and  not  far  removed  from  the  center.  Such  a  condition  can  be  real- 
ized if  one  places  in  front  of  the  lens  a  diaphragm  which  excludes  all 
light  except  that  passing  through  the  center  of  the  lens  and  if  the  field 
of  view  is  small.  But  such  a  diaphragm  lets  so  little  light  through 
that  the  image  for  most  purposes  is  not  sufficiently  bright.  If  the 
course  of  the  rays  through  a  lens  is  traced  exactly  and  no  approxi- 
mations are  made,  it  is  found  that  in  general  there  is  no  single  point 
through  which  all  the  rays  pass  after  refraction  by  a  lens.  All  the 
rays,  however,  pass  relatively  near  the  image  point  which  was  located 

by  the  approximate  method.  This 
failure  of  the  rays  to  pass  through  a 
single  point  after  refraction  gives 
rise  to  a  lack  of  perfection  in  the 
image  which  is  said  to  be  due  to  the 
presence  of  aberrations.  As  a  result 
^    ,.,    ^  ,       ,  ,      ^  of  the  aberrations,  a   point  in   the 

Fig.  43.— Spherical  aberration.  _  '  f 

object  corresponds,  not  to  a  point 
in  the  image,  but  to  a  small  area.  In  this  regard,  the  image  is  analo- 
gous, in  some  respects,  to  a  mosaic  made  up  of  small  blocks.  It  is 
desirable  that  the  blocks  of  the  mosaic  be  made  as  small  as  possible, 
as  details  of  the  object  which  fall  within  a  single  block  can  not  be 
distinguished.  It  thus  becomes  the  problem  of  the  instrument 
designer  to  so  design  the  optical  system  of  an  instrument  that  the 
aberrations  shall  not  be  sufficiently  great  to  make  vision  through  the 
instrument  unsatisfactory. 

The  aberrations  of  a  lens  arise  from  several  different  causes  and 
for  convenience  each  is  spoken  of  as  producing  a  specific  type  of 
aberration  although  the  aberrations  seldom  exist  independently. 
The  aberrations  most  commonly  considered  as  distinct  are  spherical 
and  chromatic,  coma,  astigmatism,  distortion,  and  curvature. 

Spherical  aberration. — Figure  43  illustrates  the  formation  of  an 
image  by  a  lens  when  there  is  a  large  amount  of  spherical  aberration. 
The  rays  which  pass  through  the  center  of  the  lens  and  those  near 
the  edge,  after  refraction,  do  not  cut  the  axis  at  a  single  point.  If  the 
lens  is  a  single  positive  lens,  the  rays  farther  from  the  center  cut  the 
axis  nearer  the  lens  than  the  center  rays.  For  a  negative  lens  the 
variation  is  in  the  opposite  sense.  If  we  choose  an  appropriate  non- 
spherical  surface  of  revolution,  the  rays  may  be  caused  to  cut  the 
axis  of  the  lens  at  one  point.     From  this  standpoint;  then,  the  aber- 


41 

ration  may  be  said  to  be  due  to  the  fact  that  the  lens  is  spherical  and 
it  is  therefore  termed  spherical  aberration.  The  spherical  aberration 
can  also  be  eliminated  by  combining  a  positive  and  negative  lens  to 
make  a  single  compound  lens.  As  the  aberrations  of  the  lenses  are 
in  opposite  directions  they  may  be  made  to  neutralize  each  other  in 
this  manner.  A  large  astronomical  telescope  usually  has  a  surface, 
which  by  local  polishing  is  caused  to  depart  from  the  spherical  form 
in  order  to  make  the  elimination  of  spherical  aberrations  more  perfect 
than  can  be  secured  bj  the  use  of  two  lenses.  The  chief  application 
of  the  nonspherical  surface  in  military  equipment  is  in  the  search- 
light mirror,  already  described.  It  is  desired  that  the  rays  from  the 
arc,  after  reflection  from  the  mirror,  shall  emerge  in  a  parallel  beam. 
This  requires  freedom  from  spherical  aberration  and  is  secured  by 
making  the  reflecting  surface  of  the  mirror  a  paraboloid  of  revolution. 
In  fire-control  instruments,  the  spherical  aberration  is  commonly 
eliminated  by  the  use  of  a  positive  and  negative  lens  combined. 

CTiromatic  aberration. — The  focal  length  of  a  lens  has  been  shown 
to  be 

1 


(n-1) 


K4] 


Since  n,  the  refractive  index  of  the  glass  of  which  the  lens  is  con- 
structed, is  different  for  each  color,  it  follows  that  a  lens  has  a  differ- 
ent focal  length  for  each  color  of  the  spectrum.  Consequently  even 
though  spherical  aberration  is  eliminated,  the  rays  of  different  color 
will  be  brought  to  a  focus  at  different  points.  For  a  simple  positive 
lens  the  focal  length  is  shorter  for  blue  than  for  red  light.  Like 
spherical  aberration,  chromatic  aberration  is  eliminated  by  making 
a  lens  of  two  separate  lenses,  one  positive  and  one  negative,  placed 
together.  The  positive  lens  is  made  of  a  crowTi  glass  and  the  nega- 
tive lens  of  flint.  The  fundamental  characteristic  of  flint  glass  is 
that  the  index  of  refraction  varies  much  more  for  the  different  colors 
than  is  the  case  with  the  crown.  The  negative  flint  lens  is  so  designed 
that  its  variation  of  focal  length  with  color,  which  is  in  the  opposite 
sense  to  that  of  the  crown,  is  sufficient  to  compensate  for  the  varia- 
tions in  the  crown  lens.  But  since  the  flint  glass  is  used  the  negative 
lens  does  not  neutralize  the  convergent  effect  of  the  crown  component. 
The  two  lenses,  together,  therefore  constitute  a  convergent  lens  with 
the  chromatic  aberration  eliminated.  It  is  the  usual  practice  to 
make  the  two  adjacent  surfaces  of  the  components  of  the  same 
curvature  so  that  they  may  be  cemented  together  with  Canada 
balsam,  a  transparent  cement.  This  reduces  the  loss  of  light  by 
reflection  at  the  two  surfaces  and  makes  of  the  two  lenses  a  single 
unit,  the  parts  of  which  are  not  subject  to  relative  displacement. 
In  hot  or  humid  climates  the  Canada  balsam  deteriorates  and  it  is 


42 

necessary  to  have  the  lenses  taken  apart  and  recemented  from  time 
to  time. 

Astigmatism. — Figure  44  shows  the  manner  in  which  an  image  of  a 
point  is  formed  by  a  pencil  of  light  proceeding  from  a  converging  lens 
when  affected  by  astigmatism.     If  no  aberrations  are  present  the 


/f^ 

^ 

,— -1:=^^ 

^^ 

1  •/ 

s»— — — — 

^-.E^^^^^ 

.--''^'^ 

"Y 

if 

1^ 

--^^^^"""^ 

b^ 

'^ 

h 

:i^ 

^^^^        ^^..--^ 

^^'^ 

-■'^ -^ 

\ 

^ 

If-^^ 

"-" 

"^ 

v^ 

' 

Fig.  44.— Astigmatism. 

course  of  the  rays  in  the  neighborhood  of  the  image  is  as  shown  in 
figure  45.  Cross  sections  of  the  pencil  of  light  at  several  intervals 
are  given  and  it  is  noticed  that  they  are  circular  in  form.  The  best 
image  will  be  found  at  A,  where  all  the  rays  pass  through  a  point. 
Many  times  the  rays  are  not  so  symmetrically  arranged  but  approach 


Ooo    ooO 


Fig.  45.— Image  of  a  point.    No  astigmatism  present. 

the  condition  shown  in  figures  44  and  4G.  To  secure  clearness,  some 
of  the  rays  are  omitted  in  the  perspective  dra^nng  but  reference  to 
the  series  of  cross  sections  show  that  the  rays,  instead  of  passing 
through  a  single  point,  pass  through  two  short  straight  lines  which 
are  perpendicular  to  each  other,  as  shown  at  B  and  C.     Midway 


43 

between  these  two  lines,  at  1),  the  cross  section  is  approximately  cir- 
cular. When  the  image  is  formed  by  a  bundle  of  rays  of  tliis  type, 
we  say  that  astigmatism  is  present,  and  the  image  is  said  to  be  astig- 
matic. A  lens  which  produces  an  image  without  this  fault  is  said  to 
be  anastigmatic,  i.  e.,  without  astigmatism. 

The  effect  of  astigmatism  upon  the  images  of  horizontal  and  ver- 
tical lines  is  interesting.  Consider  the  image  of  a  horizontal  line  as 
formed  in  the  plane  of  B  (fig.  46).  If  the  line  is  as  at  E  (fig.  47),  the 
image  of  each  point  of  the  line  will  be  a  short  vertical  line.  There- 
fore the  image  of  the  entire  lines  will  be  as  showTi  at  F.  The  image 
will  be  broad  and  with  ill-defined  edges.  In  the  plane  of  C  (fig.  46) 
the  image  of  each  point  will  be  a  short  horizontal  line  and  the  com- 
posite image  of  the  entire  line  built  up  of  these  partial  images  will  be 
the  sharply-defined  lines  as  sho\vn  at  G.     With  a  vertical  line,  the 


O  o 


D 


C 


Fig.  4f).— Image  of  a  point.    Astigmat  i^m  present. 


opposite  is  true.  The  sharp  well-defined  image  shown  at  I  is  in  the 
plane  of  B  (fig.  44) ,  the  hazy  image  in  the  plane  of  C.  Therefore  a 
series  of  orthogonal  lines  form  a  convenient  test  object  for  astig- 
matism. Either  vertical  or  horizontal  lines  can  be  focused  sharply, 
but  both  can  not  be  focused  simultaneously.  As  for  the  other  aber- 
rations, astigmatism  is  lessened  by  the  use  of  different  kinds  of  glass 
and  of  several  spherical  surfaces  bearing  the  proper  relation  to  each 
other.  The  cross  section  at  D  in  figure  44  which  is  nearly  circular  in 
shape  is  termed  the  ''circle  of  least  confusion,"  and  it  is  in  this  plane 
that  the  most  satisfactory  image  is  secured  when  the  object  is  an 
average  object  and  does  not  consist  of  lines  running  in  a  prevailing 
direction.  A  lens  constructed  with  ordinary  care  will  not  show  any 
astigmatism  for  a  point  on  the  optical  axis  of  the  lens  but  only  for 
points  off  the  axis. 

Coma. — If  the  different  portions  of  tlie  cone  of  rays  in  the  neigh- 
borhood of  the  image  come  to  a  focus  in  approximately  the  same 


44 


IM^^^^      r 


H 


plane,  but  fall  at  clifTerent  points  instead  of  being  superposed,  we  have 
coma. 

Figure  48  shows  such  an  image.  The  lens  may  be  considered  as 
divided  into  circular  concentric  zones.  The  inner  zone  forms  the  well- 
defined  image  at  A.     The  image  formed  by  the  next  zone  is  the  small 

circle  to  the  right  of  A.     The  image 
'  ~  L_      formed  by  each  successive  zone  is  a 

slightly  larger  circle,  displaced  to 
the  right.  The  final  image  is  as 
shown  at  C.  The  resemblance  to  a 
comet  gives  rise  to  the  name  of  this 
aberration.  The  symmetry  of  the 
lens  is  such  that  this  displacement 
of  the  successive  images  is  always 
in  a  direction  radiating  from  or 
toward  the  center  of  the  field  of 
the  lens.  Like  astigmatism,  coma 
occurs  at  the  edge  of  the  field 
rather  than  at  the  center.  It  should 
be  borne  in  mind  that  in  dealing 
with  astigmatism  and  coma  the 
simplest  possible  cases  have  been 
treated  in  which  it  was  assumed 
that  all  other  aberrations  were  ab- 
sent. The  image  of  a  point  formed 
by  a  lens  when  viewed  by  a  micro- 
scope is  usually  found  to  be  affected 
simultaneously  by  all  types  of  aber- 
rations and  often  has  a  very  fantastic  shape  only  remotely  resembling 
those  discussed. 
'  Curvature. — The  two  remaining  aberrations  to  be  discussed,  curva- 
ture and  distortion,  differ  fundamentally  from  the  first  four.  Spher- 
ical and  chromatic  aberration,  astigmatism  and  coma  have  to  do  with 
the  imperfection  of  the  image  of  a 
point.  Curvature  and  distortion 
are  aberrations  in  which  the  rela- 
tive location  of  the  images  of  dif- 
ferent points  are  incorrect  while  the 
perfection  of  the  separate  image 
point  is  not  considered.  The 
images  of  the  different  points  of  a  plane  image  should  be  in  one 
plane.  However,  oftentimes  they  lie  on  a  curved  surface  with  the 
points  at  the  edge  of  the  field  l3^ing  nearer  the  lens  than  those  at 
the  center.  (See  fig.  49.)  This  is  particularly  disadvantageous  in 
a   photographic   lens.     The   photographic   plate   is   plane    and    the 


■ 


I 


Fig.  47.— Astigmatic  images. 


45 

image,  if  it  is  to  be  in  focus  on  the  whole  phite  at  once,  should 
also  be  plane.  A  field  without  curvature  is  termed  "flat."  Flatness 
of  field  is  secured  by 
the  use  of  particular 
kinds  of  glass  and 
by  means  of  dia- 
phragms which 
cause  the  rays 
forming  images  at 
the  edge  and  cen- 
ter of  the  field  to  traverse  different  portions  of  the  lens. 

Distortion. — Figure  50  shows  the  image  of  an  object  viewed  through 
a  lens  which  produces  distortion.     Any  straight  line  extending  across 


Fig.  49.— Curvature  of  field. 


jO.— Dislurli 


the  field  is  curved  and  for  different  lenses  the  curvature  may  be  from 
or  toward  the  center.     The  distortion  is  termed  *' barrel-shaped  "  in 


46 

the  first  case  and  "hourglass"  or  "pincushion"  in  the  second.  The 
two  lower  diagrams  show  the  appearance  of  a  net  of  orthogonal  lines 
when  imaged  by  a  lens  affected  with  either  type  of  distortion.  Such 
an  object  is  frequently  used  as  a  test  object  to  determine  the  amount 
and  character  of  distortion  present. 

RESOLVING   POWER. 

A  study  of  the  physical  nature  of  light  shows  that  it  is  a  wave 
phenomenon.  It  is  a  commonly  observed  fact  that  the  ocean  waves 
break  around  the  end  of  a  breakwater  and  invade  the  portion  of  the 
surface  which  would  be  completely  sheltered  if  the  waves  traveled 
only  in  a  straight  line.  In  a  similar  manner,  an  opaque  body  may  be 
considered  as  a  "breakwater"  sheltering  the  portions  which  lie 
within  the  shadow  from  the  action  of  the  light  waves.  And  further- 
more, a  careful  study  of  the  boundary  of  the  shadow  will  show  that 
to  a  very  shght  extent  the  light  waves  bend  in  around  the  edge  of  the 
opaque  object  and  invade  the  portion  which  we  should  expect  to  lie 

within  the  shadow. 

With  waves  on  the  water  this  action  is  relatively 
large,  as  the  successive  waves  do  not  follow  each 
other  closely.     Light  waves  succeed  each  other  so 
rapidly  that  the  angular  extent  of  the  bending, 
except  in  special  test  cases,  is  very  slight.     Phe- 
nomena of  this  sort  are  said  to  be  due  to  diffrac- 
tion.    It  follows   that  some   of  the  conclusions 
which  have  been  developed  regarding  the  aber- 
rations   are    very    useful    approximations,   but    are   not   rigorously 
accurate,  as  the  effects  of  diffraction  enter  as  disturbing  elements 
and  were  not  taken  into  account. 

Referring  to  figure  45,  the  image  at  A  is  shown  as  a  geometrical 
point.  Such  will  not  be  the  case  even  though  all  the  spherical 
aberration  is  eliminated.  As  a  result  of  diffraction,  the  image  is  a 
small  disk  surrounded  by  a  series  of  concentric  rings  which  rapidly 
fall  off  in  intens-ity,  as  shown  diagrammatically  on  a  greatly  enlarged 
scale  in  figure  51.  It  follows  that  details  in  the  image  which  are  less 
than  the  diameter  of  the  central  disk  can  not  be  distinguished. 
After  the  aberrations  have  been  brought  beneath  a  certain  limit,  the 
diameter  of  this  disk  can  be  further  decreased  only  by  enlarging  the 
size  of  the  lens.  When  two  near  points  viewed  through  a  lens  are 
so  close  together  that  they  can  not  be  distingushed  as  two  d'  t 
points,  it  is  said  that  they  are  not  resolved  or  that  they  are  so  close 
together  as  to  make  separation  impossible  without  the  use  of  a  lens 
of  greater  resolving  power.  The  angle  subtended  by  two  points 
which  are  just  far  enough  apart  to  permit  resolution  is  commonly 
used  as  the  measure  of  the  resolving  power  and  is  termed  the  limit- 
ing angle  of  resolution. 


If  the  aberrations  arc  reduced  to  such  an  extent  that  they  do  not 
affect  the  resolving  power  and  if  the  rays  are  parallel  and  incident 
upon  a  lens  of  diameter  d  (measured  in  inches),  then  the  limiting 
angle  of  resolution  in  seconds  denoted  by  r  will  be  given  by  the 
equation: 

-^  »"  . 

If  the  aberrations  are  not  suitably  corrected,  the  resolving  power 
may  be  less  than  that  indicated.  The  larger  the  value  of  d,  the 
smaller  is  the  limiting  angle  of  resolution  and  the  greater  the  resolving 
power.  Diffraction  therefore  sets  an  ultimate  limit  to  the  sharpness 
of  image  formed  by  a  lens  of  a  given  size  beyond  which  it  is  impossible 
to  go.  It  also  estabhshes  a  limit  beyond  which  the  further  elimina- 
tion of  aberrations  is  unprofitable.  In  practice,  the  resolving  power 
is  made  so  great  that  the  resulting  lack  of  sharpness  is  too  slight  to 
be  perceived  by  the  eye. 

THE   TELESCOPIC    SYSTEM. 

The  optical  system  illustrated  in  figure  52  consists  of  two  con- 
verging lenses  of  focal  length  /j  and  fn,  respectively,  separated  by 
the  distance  f^+f-^-  Let  it  be  assumed  that  the  object  is  to  the  left 
of  the  system  and  so  far  removed  that  the  rays  proceeding  from  any 
one  point  may  be  considered  as  sensibly  parallel.  The  rays  AG, 
BH,  and  CI  are  representative  of  a  bundle  of  parallel  rays  originating 
at  the  point  of  the  object  lying  on  the  axis  of  the  lens  system.  As 
the  rays  are  parallel,  the  image  of  this  point,  formed  by  the  first 
lens,  is  at  L.  After  passing  through  L  the  rays  are  received  by 
the  second  lens,  termed  the  eyepiece,  and  since  the  point  L  is  dis- 
tant /.  from  this  lens,  the  rays  are  rendered  parallel  and  finally 
emerge  along  lines  MS,  NT,  and  OU. 

The  rays  DG,  EH,  and  FI  are  representative  of  a  bundle  of  parallel 
rays  proceeding  from  a  second  point  of  the  object  lying  at  such  a 
distance  from  the  axis  that  the  two  points,  viewed  from  the  center 
of  the  objective,  subtend  the  angle  BHE.  The  image  of  this  point 
lies  on  the  prolongation  of  EH,  a  line  passing  through  the  optical 
center  of  the  lens.  Furthermore,  since  the  object  is  at  an  infinite 
distance,  the  image  must  lie  in  a  plane  through  L  perpendicular  to 
the  optical  axis.  (It  is,  of  course,  assumed  that  the  curvature  of 
field  is  so  slight  that  it  may  l)e  neglected.)  The  image  is  therefore 
located  at  the  point  K  and  the  path  of  rays  DG  and  FI  after  refrac- 
tion is  along  lines  GK  and  IK. 

Since  K  is  in  the  focal  plane  of  the  eyepiece,  the  pencil  of  rays 
passing  through  K,  after  the  second  refraction,  will  form  a  bundle 
of  parallel  rays.  To  determine  the  direction  of  this  l)un(lle  of  rays, 
draw  the  fictitious  ray  KZ  passing  tlu'ough  the  optical  center  of  the 


48 

second  lens.  As  it  passes  through  the  optical  center  it  will  not  be 
deviated.  But  all  rays  passing  through  K  are  parallel  after  refrac- 
tion.    Therefore  rays  PV,  QW,  and  RX  may  be  drawn  parallel  to  KZ. 

The  two  bundles  of  parallel  rays  selected  or  any  other  bundles 
•originating  at  the  distant  object,  after  passing  through  the  entire 
system,  emerge  as  bundles  of  parallel  rays.  The  object  was  at  an 
infinite  distance.  But  since  the  emergent  rays  are  parallel,  the 
image  is  also  at  an  infinite  distance.  It  at  first  seems  paradoxical 
that  such  a  system  can  have  any  use  since  both  object  and  image 
are  at  an  infinite  distance. 

However,  important  modifications  have  been  introduced,  the  most 
important  of  which  is  the  change  of  angle  between  any  two  bundles 
before  and  after  passage  through  the  system.  The  angle  between 
the  two  incident  bundles  is  BHE.  The  corresponding  angle  between 
the  two  emergent  bundles  is  TNZ.  It  is  evident  from  the  drawing 
that  the  angle  between  the  two  bundles  has  been  greatly  increased 


Fig.  52.— Telescopic  system. 

by  passage  through  the  system.  Two  points  in  the  object  which 
subtend  a  relatively  small  angle  when  viewed  by  the  naked  eye  will 
subtend  a  much  larger  angle  viewed  through  the  system.  As  in- 
creased angular  size  is  associated  with  nearness  of  the  object,  the 
use  of  such  a  system  makes  the  object  appear  nearer  to  the  observer. 
It  is  by  use  of  a  combination  of  this  type  that  the  telescope  serves  to 
magnify  a  distant  object.  The  ratio  of  apparent  size  of  an  object 
viewed  through  a  telescope  to  the  size  as  viewed  by  the  unaided 
eye  is  termed  the  magnification  or  the  power  of  the  telescope.  This 
ratio  is  identical  with 


tan  TNZ 
tan  BHE 


which  equals 


tan  KNL 
tan  KHL' 


Furthermore,  it  is  easily  seen  that 

tan  KNL  _    /, 
tan  KHL       /. 


49 

The  negative  sign  is  introduced,  as  one  of  the  angles  is  negative 
with  respect  to  the  other.  If  the  power  or  magnification  is  denoted 
by  a,  we  have 


(42) 


Before  incidence  the  bundle  embracing  rays  DG,  EH.  and  FI  is 
proceeding  from  below  upward.  After  refraction  by  both  lenses 
this  bundle  is  proceeding  downward.  Any  point  which  appears 
below  the  axial  point  when  viewed  by  the  naked  eye  appears  above 
when  viewed  through  the  telescope.  Therefoi;-e,  the  image  is  an 
inverted  one.  Points  to  the  right  and  left  are  similarly  interchanged, 
and  it  is  evident  that  this  is  true  inversion  and  not  reversion.  This' 
inversion  may  be  considered  as  indicated  by  the  negative  value  of 
a  yielded  by  eciuation  42. 

The  cross  section  of  the  bundle  of  rays  before  and  after  passage 
through  the  system  is  greatly  changed.  The  entering  bundle  has 
the  diameter  GI.     The  diameter  of  the  emergrent  bundle  is  MO.     If 


(43) 


Fig.  53.— Galilean  telescopic  system. 

the  two  diameters  arc  denoted,  respectively,  by  rf,  and  tZ,.  it  is  easily 
seen  that 

Equations  38,  39,  and  40  give  the  focal  length  and  location  of 
principal  points  for  a  system  composed  of  two  lenses.  But  s  =/i  +/,. 
Therefore,  in  all  these  expressions  the  denominator  vanishes  for  the 
particular  combination  which  has  been  discussed.  The  focal  length 
of  the  system  is  infinite,  and  the  principal  points  lie  at  the  infinitely 
distant  points  of  the  axis.  This  is  the  fundamental  characteristic 
of  the  telescopic  system.  The  telescopic  system  may  therefore  be 
defined  as  any  optical  system  of  infinite  focal  length  with  the  prin- 
cipal points  at  an  infinite  distance.  The  particular  case  illustrated 
in  figure  52  is  one  of  the  simplest  of  many  possible  variations. 

An  important  variant  is  the  Galilean  type  of  telescopic  system 
shown  in  figure  53.  The  positive  eyepiece  is  replaced  by  a  diverging 
48918°— 21 4 


50 


Ions.  As/,  is  negative,  the  eyelens  is  placed  between  the  objective 
and  its  focal  plane,  thus  making  the  distance  between  the  two  lenses 
equal  to  the  algebraic  sum  of  /  and  f^-  The  image  formed  by  the 
objective  is  at  KL.  This  image  is  only  virtual  as  the  rays,  before 
reaching  KL,  are  received  by  the  eyepiece.  Since  KL  is  in  the  focal 
plane  of  the  eyepiece,  the  pencil,  after  passing  through  both  lenses, 
proceeds  as  a  bundle  of  parallel  rays. 

The  axial  bundle  of  rays  is  easily  traced  as  it  continues  along  the 
axis  of  the  system.  As  in  the  preceding  case,  the  dh'oction  of  the 
oblique  bundle  may  be  located  by  drawing  a  ray  through  K  and  the 


Fig.  51.— Telescopic  system. 

optical  center  of  the  eye  lens.  The  emergent  bundle  wdll  be  parallel 
to  this  ray. 

If  figures  52  and  53  arc  compared,  it  will  be  seen  that  in  figure  52 
the  oblicjue  bundle,  after  passing  through  the  system,  proceeds  from 
the  left  do\vnward,  while  in  53  the  corresponding  bundle  proceeds 
from  the  left  upward.  The  telescope  shown  in  figure  52  was  an  in- 
verting telescope.  In  53  an  erecting  telescope  has  been  secured  by 
the  use  of  the  negative  eye  lens. 

A  telescopic  system  of  the  elementary  type  shown  in  figures  52 
and  53  is  not  particularly  useful,  as  the  relatively  small  number  of 
surfaces  makes  it  impossible  to  secure  a  very  satisfactory  adjustment 
of  the  aberrations.     In  ordinary  practice,  each  component,  as  above 


Galilean  telescopic  system. 


described,  is  replaced  by  a  lens  system,  in  which  case  the  distance 
from  the  second  principal  point  of  the  first  system  to  the  first  prin- 
cipal point  of  the  second  system  is  made  equal  to  the  sum  of  the 
ec[uivalent  focal  lengths  of  the  two  systems.  The  inverting  telescope 
and  Galilean  telescope,  as  actually  constructed,  are  shown  in  figures 
54  and  55. 

For  astronomical  work,  one  of  the  two  elements  may  be  a  spherical 
mirror  instead  of  a  lens.  Such  a  telescope  is  termed  a  "reflecting" 
telescope  when  it  is  desired  to  distinguish  it  from  the  refracting  tele- 
scopes in  which  lenses  are  employed.     The  largest  astronomical  tele- 


51 


scopes  are  of  the  reflecting  type,  as  it  has  not  yet  been  found  possible 
to  produce  the  very  hirge  discs  of  ghiss  sufficiently  homogeneous  for 
the  construction  of  lenses,  although  the  less  severe  requirements  to 
be  met  by  glass  destined  for  use  in  the  construction  of  mirrors  may 
be  met. 

THE   TELESCOPE   AND   THE   EYE. 

A  section  of  the  eye  is  shown  in  figure  56.  Light  entering  the  eye 
is  first  refracted  by  the  cornea,  which  is  the  strongly  curved  trans- 
parent portion  of  the  eyeball,  showTi  at  A.  The  space  B,  next  trav- 
ersed by  the  light,  contains  the  aqueous  humor.  The  cross  section 
of  the  beam  is  then  limited  by  the  iris  CC.  The  iris  is  a  diaphragm 
and  the  aperture  through  which  the  light  passes  is  termed  the  pupil. 
The  pupil  is  the  black  circular  area  of  the  eye  which  is  surrounded 
by  the  colored  annular  portion.  After  passing  through  the  pupil, 
the  light  traverses  the  crystalline  lens  D,  the  space  E  which  contains 
the  vitreous  humor,  a  jellyhke  transparent  substance,  and  the  image 
is  finally  received  upon  the  retina. 

The  retina  is  built  up  of 
microscopic  rods  and  cones 
which  are  arranged  end-on 
to  the  light  and  which 
cover  the  back  portion  of 
the  inner  concave  surface 
of  the  eyeball.  It  is  par- 
tially covered  by  a  fluid 
termed  the  visual  purple. 
The  retma  is  the  light  sen- 
sitive part  of  the  eye  and 
the  sensations  received  by  it 
optic  nerve,  showTi  at  H. 

The  function  of  the  parts  before  the  retina  is  to  produce  a  clear 
well-defined  image  of  external  objects  upon  the  retina.  For  objects 
at  different  distances,  the  focusing  of  the  optical  system  must  be 
different  if  the  images  are  to  be  equally  well  defined.  Among  optical 
instruments,  the  method  of  focusing  employed  in  the  eye  is  quite 
unique.  Ordinarily,  focusing  is  accomplished  by  altering  the  dis- 
tance between  the  optical  system  and  the  screen  receiving  the  image. 
In  the  eye,  focussing  is  performed  by  varying  the  curvature  of  the 
crystalline  lens.  Muscles  attached  to  the  periphery  pull  upon  the 
lens  until  it  becomes  flatter  or  relax  and  permit  it  to  become  more 
curved.  This  process  of  focusing  is  termed  ''the  accommodation  of 
the  eye."  The  limits  of  accommodation  are  the  two  limiting  dis- 
tances between  which  objects  must  be  placed  if  the  image  is  to  be 
sharply  focussed  upon  the  retina.  It  is  commonly  assumed  that 
the  normal  eye  can  accommodate  itself  for  any  object  lying  between 


Fig.  50.— Section  of  eye. 


ire   transmitted   to   the  brain  bv  the 


52    • 

infinity  and  a  point  about  12  inclies  in  front  of  the  eye.  Actually, 
the  limits  are  greater  than  this.  Most  eyes  can  accommodate  for  an 
object  beyond  infinity,  i.  e.,  for  a  convergent  pencil  of  light  or  for  an 
obiect  4  or  5  inches  in  front  of  the  eye.  The  limits  of  accommodation 
decrease  with  age. 

The  optical  system  of  an  eye  in  which  some  of  the  refracting  sur- 
faces are  too  strongly  curved  forms  an  image  in  front  of  the  retina. 
Under  such  conditions  the  object  will  not  be  seen  clearly.  If  the  object 
is  brought  very  close  to  the  eye,  the  image  is  thrown  back  and  may 
be  focused  upon  the  retina.  Such  an  eye  is  said  to  be  "nearsighted" 
or  myopic.  A  diverging  spectacle  lens  placed  before  the  eye  may  be 
used  to  compensate  for  the  too  strongly  curved  surfaces  of  the  eye 
and  to  permit  clear  vision  at  normal  distances. 

Conversely,  if  the  surfaces  are  too  slightly  curved,  the  image  is 
formed  back  of  the  retina.  If  the  lack  of  curvature  is  only  slight,  the 
eye  may  be  able  to  accommodate  for  far,  but  not  for  near  objects. 
Such  an  eye  is  said  to  be  "farsighted"  or  hypermetropic.  The 
remedy  is  the  use  of  a  converging  lens  to  supplement  the  too  slight 
curvature  of  the  surfaces  of  the  eye. 

Sometimes  the  surface  of  the  eye  is  not  accurately  spherical,  but  is 
curved  differently  along  different  meridians.  This  defect  is  known  as 
astigmatism.  The  effect  upon  the  image  is  similar  to  that  previously 
described  under  "Astigmatism."  It  should  be  noted  that  in  dealing 
with  lenses,  the  astigmatism  arose  from  oblique  refraction,  whereas 
in  the  case  of  the  eye  it  arises  from  a  departure  of  a  surface  from  a 
truly  spherical  form.  Astigmatism  may  be  corrected  by  the  use  of  a 
cylindrical  lens  which  is  so  turned  that  its  unequal  curvature  along 
the  different  meridians  compensates  for  the  nonuniform  curvature 
of  the  eye. 

The  iris  by  dilating  or  contracting  prevents  too  much  light  from 
entering  the  eye.  It  involuntarily  contracts  when  the  eye  is  exposed 
to  a  bright  light  and  relaxes  again  when  the  illumination  is  reduced. 
For  intense  illumination,  the  diameter  of  the  pupil  is  approximately 
one-tenth  of  an  inch.  For  very  faint  illumination,  its  diameter  will 
increase  to  0.25  or  0.3  inch.  The  rubber  eye  shield  on  the  eyepiece 
of  a  fire-control  instrument  shuts  out  all  stray  light  which  would  other- 
wise enter  from  the  sides  and  as  a  result,  the  pupil  opens  up  wider  than 
otherwise.  For  dimly  illuminated  objects,  this  is  a  great  help,  as  the 
larger  pupil  permits  more  light  to  enter  the  eye. 

The  retina  is  cellular  in  construction.  If  two  points  of  an  object 
are  so  close  together  that  the  images  fall  on  a  single  cell  of  the  retina, 
it  follows  that  they  can  not  be  distinguished.  It  is  commonly  con- 
sidered that  points  subtending  an  angle  of  one  minute  are  the  closest 
that^n  bo  separated  and  this  is  the  limiting  angle  of  resolution  for 
the  JHSMMNwormal  eye,  the  different  surfaces  and  media  are  so 


53 

combined  that  the  aberrations  of  the  S3'stem  are  too  shght  to  inter- 
fere with  distinct  vision. 

The  angidar  extent  of  an  object  which  may  be  seen  sharply  at  one 
time  is  termed  the  field  of  view.  For  the  eye,  this  is  exceedingly 
small.  An  ordinary  photographic  objective  gives  a  sharply  defined 
image  corresponding  to  a  field  of  view  of  40°  to  60°  and  objectives 
constructed  for  special  purposes  have  much  greater  fields.  With  the 
eye,  however,  objects  are  clearly  seen  only  when  the  image  falls  near 
the  center  of  the  retina.     The  angle  of  view  for  distinct  vision  is  not 


Fig.  57.— The  telescopic  system  and  the  eye. 

more  than  half  a  degree.  Portions  of  the  image  falling  on  the  remain- 
der of  the  retina  are  seen  indistinctly.  The  outer  portions  serve  as  a 
finder  to  locate  objects,  after  which  the  eye  is  turned  in  its  socket 
until  the  image  falls  up(m  the  central  portion  and- distinct  vision  is 
secured.  The  mobility  of  the  eyeball  is  so  great  that  the  narrow  field 
is  not  a  handicap.  In  fact,  the  process  of  viewing  in  rapid  succession 
the  different  portions  of  an  extended  object,  is  usually  accomplished 
without  conscious  effort. 

Although  distinct  vision  is  only  afforded  by  the  center  of  the 
retina,  the  peripheral  portions  are  much  more  sensitive  to  faint  illumi- 


54 

nation.  It  is  for  this  reason  that  faint  objects  are  more  distinctly 
perceived  when  the  eye  is  turned  so  that  the  image  is  near  the  bound- 
ary of  the  retina.  A  faint  star  just  at  the  limit  of  visibility  may  be 
seen  much  better  if  viewed  ''from  the  corner  of  the  eye"  than  if  the 
eye  is  turned  directly  toward  it. 

The  action  of  a  telescope  in  connection  with  the  eye  is  shown  in 
figure  57.  At  A,  two  bundles  of  parallel  rays  from  two  very  distant 
points  are  shown  entering  the  naked  eye.  These  two  bundles  are 
brought  to  a  focus  at  points  E  and  F.  At  B  the  course  of  the  rays  is 
shown  when  a  telescope  is  placed  before  the  eye.  The  rays  entering 
the  eye  from  any  one  point  are  parallel  at  B,  as  well  as  at  A,  and  conse- 
quently the  eye  is  accommodated  for  an  infinitely  distant  object  in 
each  case.  It  will  be  noted  that  at  A,  E  is  above  F,  while  at  B,  F'  ig 
above.  This  illustrates  the  inversion  produced  by  the  telescope. 
The  points  on  the  retina  are  farther  apart  at  B  than  at  A,  showing 
that  the  image  on  the  retina  has  been  magnified  by  the  telescope. 

C  and  D  illustrate  the  focusing  of  the  telescope  for  eyes  not  accom- 
modated for  infinity.  A  nearsighted  eye  focuses  with  less  fatigue  for 
near  points,  i.  e.,  for  divergent  rays.  If  the  lens  nearer  the  eye  is 
moved  closer  to  the  other  lens  than  the  normal  separation,  the  rays 
from  the  telescope  will  be  divergent  and,  for  the  proper  adjustment, 
the  image  will  be  sharply  defined  upon  the  retina.  If  the  proper 
spectacle  lens  were  worn  before  the  eye,  the  eye  and  lens  would  be 
accommodated  for  parallel  rays  without  any  discomfort  and  the  ad- 
justment of  the  telescope  would  be  as  shown  at  B.  But  it  is  prefera- 
ble to  remove  the  spectacle  lens  and  secure  the  compensation  by  fo- 
cusing the  telescope  as  the  use  of  spectacles  prevents  the  eye  from 
coming  properly  up  to  the  rubber  shield  and  may  cause  the  eye  to  be 
so  far  from  the  eyepiece  of  the  telescope  that  the  field  of  view  is 
restricted.  Furthermore,  there  is  a  loss  of  light  by  reflection  at  the  two 
surfaces  of  the  spectacle  lens  which  is  eliminated  when  the  lens  is 
removed  and  the  corrections  secured  by  focusing  the  instrument. 

If  the  eye  is  such  that  it  accommodates  with  less  fatigue  for  con- 
vergent rays,  the  eye  lens  is  drawn  back  from  the  front  lens  as  shown 
at  D.  For  an  eye  seriously  affected  by  astigmatism,  the  spectacles 
should  not  be  removed,  as  no  compensating  adjustment  can  be 
secured  by  focusing  the  telescope. 

The  final  image  of  any  object  is  formed  upon  the  surface  of  the 
retina  and  therefore  has  no  genuine  relief.  The  observer,  however, 
appreciates  the  fact  that  different  objects  lie  in  different  planes  and 
is  able  to  allocate  to  each  object  its  appropriate  distance  with  an 
accuracy  depending  upon  practice.  At  least  three  elements  conspire 
to  give  relief  to  an  object.  They  are  light  and  shade,  perspective, 
and  stereovision. 

A  comparison  of  a  shaded  and  an  unshaded  drawing  shows  at  once 
the  added  relief  (hat  results  from  proper  shading.     On  the  stage  a 


55 


silhouette  of  a  round  column  with  capital,  if  properly  shaded,  resem- 
bles closely  a  true  column.  Painted  panels  correctly  shaded  are  fre- 
quently used  in  ceiling  deco- 
rations with  an  effect  com- 
parable to  that  of  true 
panels.  For  an  example  of 
perspective,  one  again  re- 
verts to  the  stage.  When  it 
is  desired  to  present  the  ap- 
pearance of  a  vast  extent 
back  of  the  stage,  a  back 
curtain,  if  painted  by  a  man 
who  understands  perspec- 
tive, and  properly  illumi- 
nated, gives  a  very  perfect 
illusion.  This  is  achieved  by 
the  combination  of  perspec- 
tive and  light  and  shade. 

The  true  stereoscopic 
effect  is  entirely  different 
and  is  based  upon  the  fact 
that  the  two  eyes  observe 
an  object  from  different 
points.  Assume  that  a  cube 
level  with  the  eyes  of  the 
observer  is  the  object.  The 
plan  is  shown  in  figure  58 
It  will  be  seen  that  the  right 
eye  sees  the  front  face  and 
a  portion  of  the  right-hand 
side,  while  the  left  eye  sees 
the  front  face  and  a  much 
foreshortened  image  of  the 
left  side.  The  two  images  are  shown  in  figure  59.  The  images  pre- 
sented to  the  two  eyes  are  different,  and  entirely  unconsciously,  as  a 

result  of  experience,  this  is  inter- 
preted in  terms  of  relief.  The  fact 
that  the  two  eyes  receive  different 
impressions  differentiates  the  true 
stereoscopic  relief  from  the  relief 
obtained  by  the  use  of  perspective 
or  light  and  shade.  Tlie  illusion 
produced  by  the  last  two  would 
persist  if  one  eye  were  closed, 
while  it  is  absolutely  necessary  that  both  eyes  be  employed  if  stereo- 
scopic relief  is  to  be  secured. 


Fig.  .W. — StPreospopip  vision. 


1 

1 
1 

Fig.  59.— Stereoscopic  picture. 


56 

When  the  distance  from  an  observer  to  an  object  exceeds  a  certain 
distance,  the  angle  subtended  by  the  two  eyes  is  so  small  that  the  im- 
ages received  by  both  eyes  are  sensibly  alike.  True  stereoscopic  efTect 
then  ceases  to  exist  and  any  appearance  of  relief  beyond  this  point  is 
due  to  perspective  or  light  and  shade.  Some  authorities  consider 
that  the  distance  at  which  the  eyes  subtend  an  angle  of  30  seconds  is 
the  limiting  distance  or  radius  of  stereoscopic  vision,  as  it  is  termed. 
The  eyes  are  separated  approximately  2.6  inches.  On  this  basis  the 
radius  of  steroscopic  vision  is  approximately  500  yards. 

If,  however,  a  pair  of  binoculars  is  employed,  the  radius  of  stereo- 
scopic vision  is  much  increased.  In  the  first  place,  if  the  binocular 
is  6  power,  an  angle  of  5  seconds  after  magnification  is  apparently 
an  angle  of  30  seconds.  Therefore,  the  radius  of  stereoscopic  vision 
with  the  binoculars  should  be  the  distance  at  which  the  eyes  subtend 
an  angle  of  5  seconds,  i.  e.,  six  times  500  or  3,000  yards.  Further- 
more, if  the  individual  telescopes  of  the  binoculars  are  of  the  Porro 
type,  the  maker  turns  the  telescopes  so  that  the  objectives  are  farther 
apart  than  the  eye  pieces.  In  other  words,  the  observer  views  the 
object  from  the  two  objectives  which  are  separated,  let  us  say,  twice 
as  far  as  the  eyes.  This,  then,  doubles  the  radius  of  stereoscopic 
vision  so  that  with  the  service  6-power  glasses  it  is  approximately 
6,000  yards.     The  formula  for  the  radius  of  stereoscopic  vision  is: 

R  =  a.  Y  500  yards  (44) 

where  a  is  the  magnification  of  the  binoculars,  Z,  is  the  distance  be- 
tween the  centers  of  the  objectives  and  Zj  is  the  distance  between  the 
eyes.  The  battery  commander's  telescope  is  a  large  binocular  tele- 
scope mounted  on  a  tripod  and  particularly  designed  to  give  a  large 
radius  of  stereoscopic  vision.  When  the  halves  are  extended  in  a 
horizontal  direction,  l^  is  approximately  27  inches.  The  power  is  10. 
Substituting  in  equation  44, 

R  =  10.  ^.  500  =  52,000  yards. 

Such  an  instrument  is  particularly  desirable  for  spotting  distant 
shots  as  the  stereoscopic  relief  aids  in  estimating  overs  and  shorts. 
A  binocular  in  which  the  distance  between  the  objectives  is  much 
greater  than  that  between  the  eyes  is  frequently  termed  a  stereo- 
binocular  in  order  to  emphasize  the  enhanced  stereoscopic  efi'ect 
which  is  thereby  obtained. 

THE   COMPONENTS   OF    THE   TELESCOPE. 

It  has  already  been  noted  that  the  telescopes  illustrated  in  figures 
52  and  53  are  useless  for  most  practical  purposes.     The  simple  lenses 


57 


do  not  provide  means  for  removing  the  aberrations  and  the  complete 
telescope  would  show  chromatic  and  spherical  aberration,  coma, 
astigmatism,  distortion,  and  curvature.  To  reduce  these  aberra- 
tions to  such  an  extent  that  they  cease  to  be  objectionable,  each 
simple  lens  is  commonly  replaced  by  a  system  of  lenses,  the  forms  for 
which  have  been  carefully  determined  by  the  designer  in  such  a  way 
that  the  aberrations  of  the  different  lenses  neutralize  each  other. 

The  lens  nearer  the  object  is  termed  the  objective.  It  is  com- 
monly made  of  two  or  three  lenses  cemented  together  or  separated 
only  slightly.  When  the  objective  is  composed  of  two  components, 
one  must  be  positive  and  the  other  negative  in  order  that  the  chro- 
matic correction  may  be  achieved.  The  positive  component  is  made 
of  crowTi  glass,  a  barium  crown  being  usually  selected.  The  negative 
component  is  made  of  flint  glass.  A  crown  glass  is  more  permanent 
than  the  softer  flint  when  exposed  to  the  weather  and  as  in  many 
types  of  instruments  the  outer  surface  of  the  objective  is  exposed. 


-I-' 


m 


'A 


B 


Fig.  60.— Types  of  telescope  objectives. 


it  is  desirable  that  the  objective  be  designed  with  the  crown  compo- 
nent toward  the  object.  For  objectives  under  three  inches  in  diam- 
eter, the  two  components  are  usually  cemented  together  \^^th 
Canada  balsam.  An  objective  of  this  type  is  illustrated  at  A  (fig. 
60).  A  cemented  objective  is  particularly  desirable  in  fire-control 
instruments,  as  there  is  then  no  danger  of  relative  displacement  of 
the  two  parts.  For  objectives  larger  than  three  inches  the  two 
components  are  not  cemented.  The  two  inner  radii  are  then  given 
different  values  as  shown  at  B  (fig.  60).  Since  there  is  one  more 
radius  of  curvature  at  the  disposal  of  the  designer  in  type  B  than  in 
type  A,  it  follows  that  a  better  correction  may  be  secured.  If, 
however,  the  most  favorable  types  of  glass  are  selected,  for  small 
objectives  there  is  not  much  choice  between  lenses  of  types  A  and  B. 
At  C  is  shown  a  cemented  objective  made  up  of  a  flint  negative  com- 
ponent placed  between  two  crown  positive  components.  This  type 
of  construction  is  adopted  when  it  is  desired  to  secure  the  best  possible 
correction  of  the  aberrations  or  when  it  is  desired  to  construct  a 


58 

high-grade  objective  from  ordinary  crown  glass  and  Hint  instead  of 
from  barium  cro^vn  and  flint,  as  is  utilized  in  the  objective  of  type  A. 
The  single  lens  at  the  eye  end  of  the  diagrammatic  telescope  is 
replaced  by  a  system  of  separated  lenses  which  collectively  make  up 
the  eyepiece.  Several  types  of  eyepiece  are  illustrated  in  figure  61. 
In  eacli  illustration  the  lens  to  the  right  is  nearer  the  eye  and  is 
termed  the  eye  lens.     The  other  lens  is  called  the  ''field"  lens  or  the 


fi-4 


HUYGHENS 


RAMSDEN 


KELLNER 


FRENCH 


SYMMETRICAL 


ORTHGSCOPIC 


Fig.  01  .—Types  of  eyepieces 


"  collective  "  lens.  The  Huyghens  and  Ramsden  eyepieces  are  each 
made  up  of  two  single  lenses.  These  types  of  eyepiece  were  used 
exclusively  in  the  earlier  telescopes  and  are  still  much  used  in  lab- 
oratory telescopes  of  low  power.  A  telescope  with  a  Huyghens 
eyepiece  can  not  be  provided  with  a  reticule  (see  below)  and  for  this 
reason  is  only  used  on  telescopes  designed  for  observation  purposes. 
The  Kellner  eyepiece  is  a  modified  Ramsden  in  wliich  the  single  eye 


59 

lens  of  the  Ramsden  type  is  replaced  ])y  a  cemented  doublet  made  up 
of  crown  and  flint  glass.  The  Kellner  eyepiece  is  one  of  the  types 
most  commonly  employed  on  fire-control  apparatus.  It  is  also 
illustrated  in  figure  54.  The  symmetrical  eyepiece  is  the  other  type 
most  common  on  fire-control  instruments.  It  is  always  employed 
on  a  telescope  which  is  designed  to  have  a  long  eye  distance  as  for  a 
sight  which  is  mounted  directly  on  the  gun.  The  French  eyepiece  - 
is  so  named  because  it  was  generally  indicated  on  French  drawings 
of  optical  instruments  furnished  us  during  the  war.  It  is  very 
similar  to  the  Kellner  eyepiece,  but  the  tlu-ee-component  eye  lens 
permits  the  use  of  ordinary  crown  instead  of  barium  crown  for  the 
positive  components.  The  orthoscopic  eyepiece  is  used  only  on 
high-power  telescopes  in  which  an  eyepiece  of  very  short  focus  is 
required.  It  is  the  eyepiece  which  is  commonly  employed  on  the 
self-contained  range  finder.  This  eyepiece  is  so  named  because  of 
its  freedom  from  distortion. 

A  telescope  designed  for  establisliing  a  line  of  sight  as  a  surveying 
instrument,  a  fire-control  instrument,  or  telescopic  sight  is  provided 
with  a  reticule.  In  a  fire-control  instrument  the  reticule  is  com- 
monly a  piece  of  plane  parallel  glass  with  a  pattern  etched  upon  it 
and  adjusted  in  the  telescope  so  that  the  plane  of  the  etched  side 
is  in  the  focal  plane  of  the  objective.  In  figure  52  the  reticule  would 
be  placed  in  the  plane  of  KL.  (The  Galilean  telescope  shown  in  / 
figm-e  53  can  not  be  fitted  with  a  reticule,  as  the  image  formed  by 
the  objective  is  virtual  and  not  real.)  In  a  surveying  instrument 
the  sturdy  construction  required  for  fire-control  apparatus  is  not  so 
necessary.  Accordingly,  the  reticule  frequently  consists  of  two 
crossed  spider  webs  or,  where  a  stadia  is  to  be  employed,  a  more 
elaborate  network  made  of  spider  web,  fine  wire,  or  quartz  fibers. 
Since  the  reticule  lies  in  the  plane  of  the  image  of  the  object,  the 
markings  of  the  reticule  appear  superposed  upon  the  target  and  there 
is  no  relative  motion  between  the  two. 

When  a  telescope  is  intended  for  use  simply  to  establish  a  line  of 
sight,  the  pattern  of  the  reticule  is  very  simple,  usually  a  pair  of 
crossed  lines.  However,  since  the  apparent  angular  dimensions  of 
the  reticuh'  remain  constant,  reticule  scales  represent  convenient 
means  for  measuring  small  angles.  The  angle  subtended  by  any 
two  points  on  the  reticule  is  tlie  angle,  the  tangent  of  which  is  d/f, 
where  d  is  the  linear  distance  between  the  two  points  in  question  and 
/is  the  equivalent  focal  length  of  the  objective.  This  formula  only 
holds  when  there  is  no  lens  between  the  objective  and  reticule  but 
is  entirely  unaffected  by  any  changes  in  the  optical  system  traversed 
by  the  light  after  passing  through  the  reticule. 

Different  types  of  reticule  are  illustrated  in  figure  02.  The  single 
pair  of  cross  wires  shown  at  A  is  used  in  the  ordinary  surveying  instru- 


60 

ment.  In  some  fire-control  apparatus,  particularly  in  that  for  use 
against  aircraft,  typo  B  or  C  is  commonly  employed.  The  fine  lines 
in  the  center  at  B  or  the  clear  center  at  C  enables  the  small  image 
of  the  airplane  to  be  seen  better  than  if  it  were  obscured  by  heavy 
crosslines.  At  the  same  time  the  outer  heavy  lines  help  to  locate 
the  center  of  the  field.  The  stadia  scale  in  a  surveyor's  transit  is 
essentially  a  scale  for  establishing  a  constant  small  angle.  The 
observer  reads  through  the  transit  the  length  of  the  stadia  rod  which 
subtends  this  small  angle.  It  is  then  a  simple  matter  to  determine 
the  distance  to  the  stadia  rod.  A  stadia  scale  is  shown  at  D.  At  E 
the  reticule  used  in  the  service  binocular  is  shown.     The  larger  inter- 


B 


D 


Fig.  62.— Types  of  reticule  designs. 


vals  of  the  horizontal  scale  are  10  mils  each.  The  vertical  scale  is  an 
inverted  copy  of  the  scale  on  the  rear  musket  sight.  The  reticule 
shown  at  F  bears  an  entire  range  scale  and  is  used  in  the  telescopic 
sight  for  tank  guns.  The  numbers  refer  to  range  in  hectometers. 
If  an  object  is  ten  hectometers  away,  the  gun  is  trained  with  the 
tenth  graduation  upon  the  target.  The  marks  are  so  spaced  that 
the  gun  is  then  automatically  elevated  correctly  for  that  range.  The 
line  is  purposely  inclined  so  that  it  makes  a  small  angle  with^the 
vertical.  As  a  result  of  this,  the  gun  is  turned  slightly  to  the  right, 
the  amount  increasing  with  increasing  range.  This  compensates 
for  the  drift  of  the  projectile  which  results  from  the  rifling. 


61 

If  the  adjustment  of  the  telescope  is  mcorrect,  there  will  be  rela- 
tive motion  between  the  target  and  the  reticule  as  the  eye  is  moved 
from  side  to  side  before  the  eyepiece.  During  this  test  the  instru- 
ment must,  of  course,  be  rigidly  supported.  This  relative  shifting 
of  target  and  reticule  is  said  toJ)e  due  to  parallax.  It  arises  because 
the  reticule  and  image  do  not  lie  accurately  in  the  same  plane. 
Parallax  can  only  be  eliminated  by  altering  the  spacing  between 
objective  and  reticule  until  the  reticule  is  brought  into  the  plane  of 
the  image.  As  any  apparent  shift  due  to  parallax  is  magnified  by 
the  eyepiece,  a  surprisingly  slight  maladjustment  will  lead  to  a 
troublesome  amount  of  parallax. 

The  telescope  with  a  reticule  is  superior  to  the  open  sight  for 
at  least  three  reasons.  The  magnification  enables  the  target  to  be 
seen  much  more  distinctly.  It  enables  the  same  accuracy  to  be 
secured  with  a  much  shorter  sighting  base  than  with  the  open  sight. 
The  two  objects  to  be  brought  into  coincidence,  i.  e.,  the  reticule  and 
target,  are  in  the  same  focal  plane,  and  the  eye  accommodates  itself 
for  both  objects  simultaneously  without  any  difficulty,  while  the  open 
sight  requires  that  the  eye  view  simultaneously  or  at  successive  inter- 
vals the  front  sight,  and  the  target  wliich  are  obviously  at  greatly 
differing  distances  from  the  eye.  Furthermore,  in  many  cases,  as 
with  the  periscopes,  the  telescope  is  so  designed  that  the  observer 
can  see  over  a  parapet  and  thus  secure  more  protection  than  with  an 
open  sight. 

For  perfect  focusing  of  a  telescope  under  all  conditions,  two  ad- 
justments are  necessary.  Means  must  be  provided  for  adjusting 
the  distance  between  reticule  and  objective  so  that  there  shall  be  no 
parallax.  This  is  usually  accomplished  by  a  rack  and  pinion  move- 
ment. If  the  focal  length  of  the  objective  is  short  and  the  targets 
are  in  general  at  a  great  distance,  the  reticule  may  be  adjusted  for  a 
target  at  an  infinite  distance  when  the  instrument  is  assembled  in  the 
factory  and  no  field  adjustment  provided  for  the  objective.  This  is> 
the  case  with  most  fire-control  instruments  and  low  power  telescopes. 
A  surveyor  frequently,  however,  has  to  take  a  sight  upon  an  object 
distant  only  a  few  feet,  and  with  a  telescope  with  a  fixed  objective, 
the  parallax  would  be  so  great  that  the  requisite  accuracy  could  not 
be  secured. 

If  the  distance  between  reticule  and  eyepiece  is  not  adjusted  for  the 
observer's  eye,  the  reticule  will  not  be  sharply  defined.  Tliis  is  the 
phase  of  focusing  illustrated  in  figure  57.  The  two  lenses  of  the 
eyepiece  are  mounted  in  a  single  tube  and  its  distance  from  the  reticule 
can  be  adjusted  by  a  rack  and  pinion,  by  a  simple  draw  tube  or  by 
rotating  the  entire  eyepiece,  causing  it  to  screw  in  or  out.  This 
adjustment  is  primarily  designed  to  enable  the  telescope  to  be 
focused  for  different  eves  and  is  referred  to  as  the  diopter  movement. 


G2 

Oh  fire-control  instruments,  a  scale  is  generally  })rovided  around  the 
eyepiece  reading  in  diopters/  by  which  the  telescope  can  be  adjusted 
directly  if  the  correction  required  by  the  eye  is  known.  The  scale 
is  graduated  from  —  5  through  0  to  5.  For  a  normal  eye,  the  eyepiece 
is  set  at  zero.  If  a  positive  2-diopter  spectacle  lens  is  commonly  worn, 
then  the  eyepiece  should  be  set  at  +2.  This,  of  course,  presupposes 
that  the  spectacles  are  removed.  It  is  usually  preferable  to  use  the 
numbers  on  the  diopter  scale  as  reference  numbers  only.  After 
having  carefully  focused  the  instrument  once,  the  reading  of  the 
eyepiece  should  be  noted  and  used  for  future  focusing. 

If  a  telescope  is  only  provided  with  a  focusing  eyepiece,  as  is  the 
case  in  most  fire-control  instruments,  very  near  objects  may  be 
focused  sharply  by  properly  adjusting  the  eyepiece.  But  there  will 
then  be  a  great  deal  of  parallax  between  reticule  and  target  which 
can  not  be  eliminated  because  of  lack  of  means  for  adjusting  the 
distance  between  reticule  and  objective.  This  parallax,  in  a  properly 
assembled  instrument,  should,  however,  vanish  when  the  instrument 
is  focused  upon  a  distant  object. 

Low-power  telescopes  are  frequently  made  without  any  means  for 
focusing.  Such  an  instrument  is  termed  a  ''fixed-focus"  telescope. 
A  fixed-focus  telescope  when  assembled  is  often  so  adjusted  that  the 
bundle  of  rays  emerging  from  the  instrument,  instead  of  being 
parallel,  appears  to  diverge  from  a  point  18  to  30  inches  in  front  of 
the  eye  lens.  It  has  been  learned  that  a  telescope  so  focused  is  more 
readily  adaptable  to  the  eye  of  the  average  observer  than  a  telescope 
focused  so  that  the  rays  of  the  pencil  are  parallel.  For  a  fire-control 
instrument,  the  fixed-focus  telescope  is  preferable,  as  the  construction 
is  much  simplified  and  the  instrument  can  be  made  entirely  waterproof. 
But  if  the  power  of  the  telescope  is  greater  than  3.5  or  4,  the  accom- 
modation of  the  average  eye  is  not  sufficient  to  permit  its  use. 

THE   TELESCOPE   WITH   AN    ERECTING   SYSTEM. 

The  inverting  telescope  as  commonly  constructed  with  a  two- 
component  cemented  objective  and  a  Kellner  eyepiece,  is  shown  in 
figure  54.  Telescopes  of  this  type  are  often  employed  in  laboratory 
apparatus  where  the  inversion  of  the  image  is  not  particularly 
troublesome.  In  fire-control  apparatus,  however,  it  is  essential  that 
all  telescopes  be  of  the  erecting  type,  as  the  observer  must  not  be 
forced  to  devote  a  portion  of  his  energy  to  the  mental  transposition 
of  an  inverted  image. 

1  In  the  diopter  system  the  "converging  power"  of  the  lens  is  measured  instead  of  the  focal  length.  A 
positive  lens  having  a  focal  length  of  1  meter  is  a  plus  1-diopter  lens.  A  lens  havijig  half  the  focal  length  has 
twice  the  converging  power  and  is  accordingly  a  2-diopter  lens.  A  negative  lens  of  1-meter  focal  length  has  a 
power  of  minus-1  diopter.    If  P  is  the  converging  power  in  diopters  and /is  the  focal  length,  measured  in 


63 


^ 


LJ 


r 

L 

r 


CD  % 


The  Galilean  telescope,  although  it  gives  an  erect  image,  is  not 
suitable  for  use  on  fire-control  instruments,  as  it  can  not  be  fitted 
with  a  reticule.  If,  in  the  telescope  showm  in  figure  54,  an  optical 
sj^stem  is  interposed  between  the  objective  and  ej^epiece,  which  will 
reinvert  the  inverted  image  formed  by  the  ob- 
jective, the  net  result  of  the  two  inversions  will 
be  an  erect  image.  This  is  the  method  adopted 
in  most  erecting  telescopes  used  for  fire  control 
and  either  a  lens  or  a  prism  system  may  be  em- 
ployed. 

A  telescope  in  which  a  lens  erecting  system 
has  been  interposed  to  erect  the  image  is  shown 
in  figure  63.  The  objective  A  forms  an  in- 
verted image  of  the  object  at  B.  The  lens 
erecting  system  at  C  is  composed  of  two  ce- 
mented achromatic  lenses.  It  forms  at  D  an 
image  of  the  original  image  formed  at  B.  This 
final  image  is  then  viewed  by  the  eyepiece  at  E. 
Often  a  plano-convex  lens  is  inserted  in  the 
system  in  the  neighborhood  of  B.  This  bends 
the  outer  rays  proceeding  from  the  objective  in 
toward  the  axis  so  that  they  will  pass  through 
the  erecting  lenses.  This  serves  to  increase  the 
field  of  view  for  a  given  diameter  of  the  lenses 
of  the  erecting  system.  Such  a  lens  is  termed  a 
"collective"  lens.  A  reticule  may  be  placed  at 
B  or  D.  It  is  much  preferable  to  place  the  reti- 
cule at  B,  as  the  objective  and  reticule  then 
form  a  unit,  and  any  shift  of  the  erecting  sys- 
tem does  not  disturb  the  line  of  collimation. 

The  objective  and  eyepiece  shown  in  figure  63 
are  the  same  as  in  figure  54  and  the  scale  of  the 
two  drawings  is  the  same.  The  increase  in 
length,  due  to  the  use  of  the  erecting  system, 
is  evident  and  this  can  jiot  be  avoided.  For  an 
instrument  to  'beTield  in  the  hand,  this  is  a  dis- 
advantage, as  the  increased  length  makes  the  in- 
strument difficult  to  hold  without  vibration.  If 
an  attempt  is  made  to  decrease  the  length  of  a 
telescope  of  this  type  by  using  an  erecting  system 
of  very  short  focus,  excessive  curvature  of  field  results  and  the  border 
of  the  field  is  very  much  blurred.  For  some  instruments  the  increased 
length  due  to  the  use  of  the  erecting  system  is  an  advantage.  This 
is  the  case  with  all  periscopes,  and  telescopes  for  this  purpose  have 
b(HMi  ])uilt  in  which  the  distance  from  objective  to  eyepiece  is  as  great 


ir-M^     <J. 


64 


as  80  feet.  The  optical  system  of  the  periscope  is  similar  to  that 
shown  in  figure  63,  with  the  collective  lens  added  at  B.  In  order  to 
secure  the  great  length,  an  erecting  system  of  long  focal  length  is 
employed  so  that  the  distance  from  B  to  D  makes  up  the  greater 
portion  of  the  length  of  the  instrument. 

When  a  lens  erecting  system  is  used,  the  magnifying  power  is  not 
correctly  given  by  formula  42.  This  formula  is  correct  when  the 
image  formed  at  B  is  viewed  directly  by  the  eyepiece,  as  in  figure  54. 
But  the  lens  system  at  C  may  enlarge  or  reduce  the  image  in  addi- 
tion to  erecting  it.  Lengths  h  and  h'  are  measured  from  B  and  D 
to  the  corresponding  principal  points  of  the  erecting  system.  The 
ratio  of  the  size  of  the  image  at  D  to  the  size  of  the  image  at  B  is  then 

—  -^  where  the  negative  sign  is  introduced  to  indicate  that  one  image 

is  inverted  with  respect  to  the  other.     The  magnification  of  the  com- 
plete telescope  is: 

The  focal  lengths  of  objective 
and  eyepiece  are  /i  and/2,  respec- 
tively. The  first  quantity  in 
parentheses  is  the  magnification 
produced  by  the  original  invert- 
ing telescope,  the  second  quan- 
tity is  the  magnification  pro- 
duced by  the  erecting  system. 
In  the  telescope  shown  in  figure 
63,  the  erecting  system  does  not  affect  the  numerical  value  of  the 
magnification,  as  h  and  6'  are  equal,  but  the  erecting  system  may, 
according  to  the  construction,  increase  or  reduce  the  magnification. 

Where  compactness  is  a  desirable  feature,  a  prism  erecting  system 
is  employed.  The  Porro  system  shown  in  figure  64  is  the  type  em- 
ployed in  prism  field  glasses  and  in  many  small  telescopes.  A  per- 
spective view  of  the  prism  system  is  shown  in  figure  19.  The  scale 
of  figure  54  and  of  the  following  figures  illustrating  the  erecting  tele- 
scopes are  the  same  as  for  figures  54  and  63.  The  great  reduction 
in  length  resulting  from  the  use  of  the  prism  system  is  apparent.  It 
will  be  noted  that  the  path  of  the  light  is  doubled  back  upon  itself 
twice  and  it  is  by  this  means  that  the  compactness  is  attained.  This 
doubling  back  of  the  ray  is  better  shown  in  figure  19  than  in  64.  In 
describing  the  lens  erecting  system,  it  was  noted  that  its  tendency 
is  to  increase  the  curvature  of  the  field.  The  prism  system  tends  to 
decrease  curvature  and  its  use,  therefore,  is  particularly  advantageous 
when  a  compact  instrument  having  a  large  field  of  view  is  desired- 


i  11 

\ 

1 
Ik 

1      N 
1      1 

^s 

V    J 

i^ 

Fig.  64.— Telescope  with  Porro  erecting  system. 


65 

A  prism  erecting  s3-stem,  either  of  this  type  or  of  the  following 
types,  does  not  alter  the  magnification  of  the  telescope.  There- 
fore, to  determine  the  magnification,  equation  42  is  used  without 
change.  The  reticule  is  placed  at  C  and  occupies  the  same  posi- 
tion relative  to  the  eyepiece  as  in  the  simple  inverting  telescope. 
If  the  line  of  collimation  is  to  be  preserved  invariant,  there  must  be 
no  movement  of  the  two  Porro  prisms  as  they  are  interposed  between 
the  objective  and  the  reticule.  If  the  telescope  is  to  be  mounted  on 
a  gun  as  a  telescopic  sight,  this  is  a  real  disadvantage,  as  the  Porro 
prisms  are  of  an  awkward  shape  and  it  is  difficult  to  clamp  them  so 
tightly  that  the}'  will  not  shift  when  the  gun  is  fired. 

In  figure  65  the  erecting  system  used  is  the  second  type  of  Porro 
prism.  A  perspective  view  of  this  is  shown  in  figure  20.  The  relative 
positions  of  the  two  upper  polished  faces  are  such  that  the  system  has 
to  be  constructed  in  two  pieces,  which  are  either  cemented  together  or 
clamped  when  properly  located  with  respect  to  each  other.  This 
type  of  prism  does  not  shorten  the  telescope  as  much  as  the  first  type 


Fig.  65. — Telescope  with  second  type  of  Porro  erecting  system 


of  Porro  prism  and  is  not  so  generall}^  employed.  At  present  it  is 
found  in  no  fii-e-control  instruments  of  American  construction,  but  is 
used  in  the  three-power  observation  telescopes  which  were  purchased 
from  the  French  Government  under  the  name  "Longue-vue- 
Monoculaire." 

For  antiaircraft  fire-control  apparatus  and  for  the  right-angle 
theodolites  used  for  observing  the  course  of  the  rubber  meteorological 
sounding  balloons,  a  right-angle  erecting  telescope  is  required.  The 
right-angle  prism  with  roof  angle  is  employed.  By  its  use  the  right 
angle  in  the  axis  of  the  telescope  and  the  erection  of  the  image  are 
secured.  Figure  66  shows  the  complete  telescopic  system.  The  per- 
spective view  of  the  prism  is  illustrated  in  figure  21. 

The  Brashear-IIastings  prism  formerly  used  in  our  large  depression 
position  finders  is  shown  in  figure  23.  Figure  67  illustrates  the  com- 
plete telescopic  system.  The  sole  advantage  of  the  Brashear- 
Hastings  prism  lay  in  the  fact  that  erection  was  accomplished  without 
any  lateral  displacement  of  the  axis  of  the  telescope.  Ileference  to 
48918°— 21 5 


66 


preceding  and  following  prism  systems  will  show  that  for  all  other 

prism  types  the 
axes  of  the 
objective  and 
telescope  do  not 
fall  along  the 
same  straight 
lines.  This  was 
thought  to 
make  it  difii- 
cult  to  quickly 
direct  the  tele- 
scope at  a  tar- 
get. The  ce- 
mented surfaces 
and   the    roof 

angle  proved  to  be  disadvantages  which  outweighed  the  advantage  of 


Fig.  66. — Telescope  with  roof  angle  erecting  prism. 


Fig.  67.— Telescope  with  Brashear-Hastings  erecting  prism. 

the  common  axis.     Accordingly,  the  Brashear-Hastings  system  has 


Telescope  with  Spreiiger  prism. 


been  discontinued  in  fire-control  instruments.     Many  times  a  small 
open  sight  is  added  to  aid  in  the  preliminary  directing  of  the  telescope. 


67 

Figure  68  illustrates  the  use  of  the  erecting  prism  shown  in  figure  24. 
This  prism  may  be  constructed  in  one  piece  and  is  of  such  shape  that 
it  may  be  rigidly  clamped  in  the  instrument.  This  makes  its  use  par- 
ticularly adyantageous  in  a  sight  to  be  mounted  directly  on  a  gun. 
There  is  a  considerable  lateral  displacement  of  the  ray.  This  may  be 
an  advantage  or  disadvantage,  depending  upon  the  particular  use  to 
which  the  instrument  is  to  be  put.  The  light  path  in  the  glass  is 
very  long,  and  as  the  prism  is  constructed  in  one  piece,  it  is  difficult 
to  secure  a  piece  of  glass  large  enough  and  sufficiently  homogeneous 
except  for  telescopes  of  the  smaller  size. 

THE   FIELD    OF   VIEW   AND    BRIGHTNESS   OF   IMAGE. 

In  figure  69  the  telescope  shown  in  figure  52  is  again  illustrated. 
The  courses  of  rays  AD,  BD,  and  CD  are  traced.  These  are  all  inci- 
dent at  different  inclinations  at  the  center  of  the  objective  and  pro- 
ceed from  different  points  of  the  object.  The  ray  BD  proceeds  from 
a  point  on  the  axis,  and  its  course  is  easily  traced  as  it  is  not  deviated 


Fig.  69.— Field  of  view  of  telescope. 

by  the  lenses  but  proceeds  along  the  straight  line  BDGHIJ.  Tliis  ray 
should  be  considered  as  representative  of  a  bundle  of  parallel  rays 
proceeding  from  the  axial  point  of  the  distant  object,  brought  to  a 
focus  at  G  and  again  converted  into  a  bundle  of  parallel  rays  by  the 
eye  lens. 

The  aperture  of  the  reticule  at  G  is  limited  by  the  diaphragm  EF. 
Ray  CD  has  been  chosen  so  that  it  just  passes  through  tliis  diaphragm. 
As  in  figure  51,  the  course  of  this  ray  after  inciden^  upon  the  sec- 
ond lens  is  obtained  by  drawing  the  auxiliary  lineCfeHN.  ^Vny  ray 
falling  upon  the  objective  at  an  inclination- greater  than  that  of  CD 
will  be  stopped  by  the  diaphragm  EF.  Ray  AD  is  representative  of 
a  bundle  of  rays  proceeding  from  a  point  of  the  object  and  this  point 
will  lie  at  the  extreme  edge  of  the  field  of  view  as  seen  through  the 
telescope.  As  diaphragm  EF  lies  in  the  focal  plane  of  the  objective, 
it  will  be  projected  upon  the  object  in  the  same  manner  that  the 
reticule  is  projected.  The  field  of  view  will  therefore  be  enclosed  by 
the  image  of  the  diaphragm  EF.  Ray  CD  is  the  ray  corresponding  to 
AD  and  symmetrically  placed  with  respect  to  BD. 


68 

The  angle  ADC  represents  the  maximum  angle  subtended  by  two 
objects  which  may  be  viewed  simultaneously  tlirough  the  telescope. 
This  is  spoken  of  as  the  true  field  of  view  of  the  telescope.  If  the 
radius  of  EF  is  r  and  angle  ADC  is  u,  then  it  is  evident  that — 

tan^/z^JJ  (46) 

J\ 

u  -  2  tan-'  Y  (47) 

J\  . 

The  rays  AD  and  CD  after  passage  through  the  telescope  subtend 
the  angle  KIL.  This  angle  is  spoken  of  as  the  apparent  field  of  view. 
If  it  is  represented  by  v,  it  may  be  said  that  objects  in  directions  DA 
and  DC  actually  subtend  the  angle  u  but  apparently  subtend  the 
angle  v.     If  a  is  the  magnification  of  the  telescope,  then — 

v  =  au  (48) 

It  should  be  noted  that  increasing  the  size  of  the  objective  does 
not  increase  the  field  of  view.  It  does  increase  the  size  of  the  indi- 
vidual bundles  of  rays  received  by  the  telescope,  as  shown  in  figure 
52,  but  the  field  of  view  is  independent  of  the  diameter  of  the  objec- 
tive. The  eye  lens  must  be  large  enough  to  receive  the  ray  CDE  or 
it  will  reduce  the  extent  of  field  below  that  given  by  the  equation. 

The  apparent  field  of  view  is  generally  limited  by  the  optical  possi- 
bilities of  the  eyepiece.  An  apparent  field  of  45°  may  be  considered  as 
a  practical  maximum  for  a  highly  corrected  eyepiece.  Thirty-five 
to  forty  degrees  is  a  more  common  value  and  in  the  more  simply 
constructed  eyepieces  the  field  may  be  only  25°  or  30°.  This,  with 
equation  48,  determines  a  maximum  value  of  the  true  field  for  any 
given  magnification.  For  example,  if  we  use  an  eyepiece  corrected 
for  an  apparent  field  of  40°  and  have  a  ten-power  telescope,  the  maxi- 
mum true  field  will  be  4°.  If  the  telescope  has  an  erecting  system 
of  any  type,  the  components  must  be  designed  sufficiently  large  to 
transmit  all  the  rays  indicated  in  figure  69,  otherwise  the  erecting 
system  will  decrease  the  field  of  view  as  determined  by  the  fore- 
going analysis. 

In  figure  69  the  rays  which  are  traced  cross  at  the  point  I.  It  is 
evident  that  D  and  I  are,  respectively,  object  and  image  points  with 
respect  to  the  eyepiece.  Reference  to  figure  52  shows  that  at  this 
point  the  cone  of  rays  proceeding  from  the  telescope  has  the  minimum 
diameter.  The  eye  should  be  so  placed  that  the  pupil  is  brought  to 
this  point.  If  a  telescope  is  held  ten  or  fifteen  inches  from  the  eye 
and  pointed  at  a  bright  source  of  light,  a  brightly  illuminated  disk 
will  be  seen  a  short  sistance  in  front  of  the  eyepiece.  This  disk 
occupies  the  position  at  Y  in  figure  52  and  I  in  figure  69.  It  is  termed 
the  exit  pupil  and  is  the  image  of  the  objective  formed  by  the  eyepiece. 


69 

Referring  to  figure  53,  it  is  seen  that  the  emergent  bundles  of  par- 
allel rays  cross  at  a  point  between  the  eye  lens  and  the  objective. 
It  is  desirable  to  bring  the  pupil  of  the  eye  to  this  point  but  this 
obviously  can  not  be  done  as  the  location  of  the  eye  lens  prevents  it. 
The- exit  pupil  in  this  case  is  virtual.  This  follows  naturally  as  the 
exit  pupil  is  the  image  of  the  objective  formed  by  the  eyepiece  antl, 
if  the  eyepiece  is  negative,  the  image  of  the  objective  is  necessarily 
virtual.  Since  the  eye  can  not  be  brought  to  the  exit  pupil,  the  field 
of  view  is  very  much  restricted  and  equation  47  does  not  apply. 
For  the  Galilean  telescope  the  field  of  view  is  increased  when  the 
objective  is  enlarged.  In  order  to  secure  a  satisfactory  field  of  view 
with  tliis  type  of  telescope,  it  is  necessary  to  make  the  objective 
much  larger  than  is  conmaonly  employed  in  telescopes  of  type  shown 
in  figure  52. 

A  consideration  of  figure  70  will  make  clear  the  simple  relationship 
existing  between  the  brightness  of  an  object  viewed  with  the  naked 
eye  and  through  a  telescope.  The  telescope,  with  the  objective  as 
limited  by  the  full  lines,  is  so  constructed  that  the  diameter  of  the 
pencil  delivered  to  the  eye  is  the  same  as  that  of  the  pupil.     To  make' 


Fig.  70.— Restriction  of  the  rays  by  the  pupil  of  the  eye. 

the  illustration  more  concrete,  assume  that  the  telescope  magnifies 
two  times.  Then,  by  reference  to  equation  43,  it  is  seen  that  the 
entrance  pupil,  i.  e.,  the  diameter  of  the  unobstructed  portion  of  the 
objective,  is  twice  that  of  the  pupil  of  the  eye.  Since  the  area  of  the 
objective  varies  as  the  square  of  its  diameter,  four  times  as  much 
light  enters  the  telescope  from  a  given  small  object  as  would  enter 
the  naked  eye.  But  the  telescope  magnifies  two  times  and  therefore 
the  light  forms  an  image  on  the  retina  having  four  times  as  great 
an  area  as  that  of  the  image  formed  by  the  unaided  eye.  As  the 
telescope  collects  four  times  as  much  light  and  distributes  it  over  four 
times  the  area  on  the  retina,  it  follows  that  the  image  has  the  same 
brightness  per  unit  area  as  though  the  telescope  were  not  used.  This, 
however,  represents  the  ideal  case.  In  practice  there  is  always  a 
considerable  loss  of  light  by  absorption  in  the  lenses  and  reflection 
at  the  surfaces  which  will  seldom  amount  to  less  than  25  per  cent 
and  may  be  as  much  as  75  per  cent  of  the  incident  light. 

It  follows  that  where  the  objective  is  enlarged  to  such  an  extent 
that  the  emergent  beam  fills  the  pupil  of  the  eye,  there  is  no  further 
gain  in  illumination  to  be  secured  by  enlarging  the  objective.  The 
result  of  enlarging  the  objective  beyond  this  point  is  illustrated  in 


:/ 


70 

figure  70.  The  light  which  enters  the  telescope  through  the  portion 
of  the  objective  bounded  by  the  full  lines  enters  the  eye.  If  the  lens 
is  enlarged  as  indicated  by  the  dotted  lines,  it  is  true  that  more  light 
enters  the  telescope,  but  the  additional  light  is  prevented  from  enter- 
ing the  eye  by  the  iris. 

To  determine  the  proper  diameter  of  the  objective  of  a  telescope 
it  is  necessary  to  know  the  diameter  of  the  pupil  of  the  eye.  At 
night  the  pupil  may  dilate  until  its  diameter  is  from  0.25  to  0.3  inch. 
A  telescope  for  use  at  night  should  have  an  exit  pupil  of  this  size  and 
by  equation  43  it  is  seen  that  to  meet  this  condition  the  diameter  of 
the  entrance  pupil  in  inches  must  be  from  0.25  to  0.3  times  a,  where 
a  is  the  angular  magnification  of  the  telescope.  If  the  entrance 
pupil  is  at  the  objective,  as  should  be  the  case,  this  is  the  necessary 
diameter  of  the  objective.  During  the  day,  the  diameter  of  the  pupil 
is  from  0.1  to  0.2  inch  and  the  useful  diameter  of  the  objective  is 
correspondingly  smaller.  Many  of  the  higher-power  telescopes  used 
in  fire  control  are  made  with  objectives  smaller  than  indicated  above. 
Brightness  of  image  has  been  sacrificed  in  order  to  secure  a  more 
compact  instrument.  In  comparing  the  brightness  of  image  formed 
upon  the  retina,  with  and  without  a  telescope,  the  brightness  of  the 
image  as  it  would  be  measured  b}"  a  physical  instrument  has  been 
referred  to.  Due  to  physiological  or  psychological  causes,  a  small, 
very  dimly  illuminated  object  appears  brighter  and  details  may  be 
more  easily  discerned  when  there  is  magnification,  even  though  the 
image  actually  is  no  brighter.  For  this  reason  with  a  night  glass 
there  is  a  distinct  gain  in  visibility  which  is  due  to  the  magnification 
and  which  is  often  more  than  sufficient  to  ofi'set  the  inevitable  loss 
of  light  caused  by  the  use  of  the  telescope.  In  using  a  night  glass,  as 
in  all  conditions  when  the  illumination  is  poor,  the  eye  should  be 
protected  from  all  stray  light  in  order  that  the  pupil  may  dilate  as 
much  as  possible.  If  a  monocular  instrument  is  used,  the  eye  not 
in  use  should  also  be  shielded  from  the  light,  as,  if  it  receives  too 
much  light,  the  pupil  of  the  eye  in  use  will  contract  sympathetically. 

THE   SELECTION   AND   USE   OF   A  TELESCOPE. 

In  a  telescope,  high  power,  a  brightly  illuminated  image,  and  com- 
pactness are  three  elements  which  mutually  oppose  each  other.  The 
advantage  of  great  magnification  is  often  overrated,  particularly  in 
instruments  designed  to  be  held  in  the  hand.  It  is  well  to  decide 
first  on  the  minimum  power  which  will  be  satisfactory.  A  compro- 
mise can  then  be  effected  between  the  two  remaining  elements.  The 
light-gathering  capacity  in  two  similar  optical  systems  depends 
upon  the  diameter  of  the  exit  pupil.  This  can  readily  be  judged  by 
pointing  the  instrument  toward  the  sky  and  looking  through  it  with 
the  eye  10  or  12  inches  from  the  eyepiece.     The  brightly  illuminated 


71 

disk  seen  in  front  of  the  eyepiece  is  the  exit  pupil.  Other  conditions 
being  eqiirtl,  the  brightness  of  the  image  varies  directly  as  the  area 
of  the  disk.  As  the  area  varies  as  the  square  of  the  diameter,  a  slight 
increase  in  diameter  of  exit  pupil  indicates  greatly  increased  bright- 
ness of  the  image.  A  large  exit  pupil  can  not  be  secured  without 
increasing  the  size  of  the  instrument  or  decreasing  the  magnification. 
In  instruments  designed  for  use  during  the  day,  the  exit  pupil  is 
generally  from  0.18  to  0.20  inch  in  diameter.  For  a  night  glass  the 
diameter  should  be  at  least  0.25  inch.  Eight  power  is  commonly 
considered  the  maximum  allowable  for  an  instrument  to  be  held  in 
the  hand,  while  six  represents  the  more  common  practice.  The  lower 
power  instrument  usually  offers  the  advantage  of  a  larger  field  of 
view. 

The  usefulness  of  a  telescope  depends  primarily  upon  the  quality 
of  definition.  It  is  not  a  particularly  difficult  matter  to  determine 
which  of  two  instruments  has  the  better  definition.  The  instrument 
should  first  be  carefully  focused.  In  focusing  an  instrument  it 
is  correct  to  focus  the  eyepiece  first.  The  telescope  should  be  turned 
toward  the  sky  and  the  eyepiece  focused  until  the  reticule  stands  out 
well  defined  and  can  be  comfortably  viewed  without  straining  the 
eyes.  If  this  is  the  only  adjustment  the  instrument  has,  a  distant 
object  viewed  through  the  telescope  should  appear  sharply  focused 
and  without  parallax. 

If  means  are  provided  for  focusing  the  objective,  the  telescope 
should  now  be  turned  toward  the  target  and  the  objective  focused 
until  there  is  no  parallax.  This  adjustment  can  be  tested  by  moving 
the  eye  from  side  to  side  behind  the  eyepiece.  Focusing  should  be 
continued  until  reticule  and  target  appear  quite  stationary  with 
respect  to  each  other.  During  this  process  the  focusing  of  the  eye- 
piece must  not  be  disturbed.  After  the  parallax  has  been  eliminated, 
if  all  has  been  correctly  done,  reticule  and  target  should  both  be  well 
defined. 

It  should  be  noted  that  the  focusing  of  the  objective  depends 
only  upon  the  distance  of  the  target,  the  focusing  of  the  eyepiece 
only  upon  the  eye  of  the  observer.  If  several  observers  are  using 
the  same  instrument  successively  upon  a  stationary  target,  difi"erent 
observers  should  alter  only  the  eyepiece  adjustment.  The  adjust- 
ment of  the  objective  should  be  the  same  for  all  observers  so  long  as 
the  single  target  or  only  very  distant  targets  are  observed. 

Suitable  test  objects  are  usually  easily  found.  Telegraph  wu^es, 
the  cross  braces  and  lattice  members  of  steel  tank  towers,  flagstaff's 
or  church  steeples  with  weather  vanes  are  all  convenient.  The 
definition  in  the  center  of  the  field  should  first  be  considered.  The 
image  should  be  very  sharp  and  well  defined.  If  the  optical  system 
contams  prisms,  it  is  well  to  select  an  object  in  which  two  well-defined 


72 

lines  crossing  each  other  are  available.  The  cross  braces  of  a  steel 
tank  tower  are  particularly  suitable.  Both  lines  should  be  sharply 
defined.  If  one  appears  slightly  hazy  or  out  of  focus,  it  indicates  the 
presence  of  astigmatism.  Wliere  this  exists  in  the  center  of  the 
field,  it  may  be  due  to  the  use  of  strained  glass  or  a  slightly  spherical 
reflecting  surface  instead  of  a  plane  surface  on  one  of  the  prisms. 

Another  test  frequently  given  for  the  definition  in  the  center  of 
the  field  is  the  manner  in  which  the  image  changes  during  the  process 
of  focusing.  If  the  image  appears  equally  sharp  for  a  considerable 
range  of  focusing,  it  generally  indicates  that  the  definition  is  equally 
poor  for  the  entire  range.  If  a  truly  sharp  well-defined  image  can  be 
secured  at  all,  it  will  persist  only  through  a  very  slight  range  of 
focusing. 

After  the  definition  in  the  center  of  the  field  is  tested  the  outer 
portions  may  be  considered.  The  image  should  be  flat;  that  is, 
aU  parts  of  the  field  should  be  well  focused  simultaneously.  In  some 
particularly  high-grade  instruments  the  definition  is  remarkably 
good  over  the  entire  field,  while  in  the  medium-grade  instruments 
the  definition  falls  off  at  the  edges.  Astigmatism  may  be  tested  at 
the  edge  of  the  field  as  well  as  at  the  center  by  observing  the  crossed 
lines,  but  if  the  field  is  satisfactorily  flat  there  will  not  be  a  detri- 
mental amount  of  astigmatism. 

Objects  near  the  center  of  the  field  should  not  be  surrounded  by  a 
fringe  of  color.  However,  nearly  all  instruments  will  show  slight 
color  about  objects  near  the  edge  of  the  field.  In  a  good  instrument 
there  should  not  be  enough  color  to  interfere  with  the  appreciation 
of  fine  detail.  To  test  distortion,  a  straight  flagpole  or  smokestack 
is  a  convenient  object.  The  telescope  should  be  turned  so  that  the 
object  is  near  the  edge  of  the  field.  If  the  image  is  curved  as  in 
figure  50,  it  indicates  the  presence   of  distortion. 

If  the  telescope  has  a  reticule  and  is  not  provided  with  means 
for  focusing  the  objective,  it  should  be  tested  for  parallax.  The 
instrument  should  be  placed  on  a  fixed  support  and  directed  at  an 
object  several  hundred  yards  distant.  As  the  eye  is  moved  from 
side  to  side  behind  the  eyepiece  there  should  be  no  relative  motion 
of  reticule  and  object.  If  there  is  motion,  there  is  parallax.  Par- 
allax may  be  removed  by  an  adjustment  which,  however,  requires  the 
disassembling  of  the  instrument  and  should  only  be  done  by  the 
maker.  If  the  instrument  has  means  for  focusing  the  objective,  the 
existence  of  parallax  only  indicates  that  the  observer  has  not  focused 
the  instrument  correctly. 

The  reticule  of  a  telescope  should  be  carefully  examined  for  the 
presence  of  fUm.  In  many  instruments  after  a  few  months'  use  a 
film  forms  on  the  reticule,  which  makes  necessary  the  disassembling 
of  the  instrument  for  cleaning.     In  its  advanced  stages  the  film  is 


73 

conspicuous  and  will  not  be  overlooked.  If  a  formation  is  beginning 
to  develop,  it  may  be  detected  in  the  following  manner:  Hold  a 
sheet  of  white  paper  or  the  palm  of  the  hand  one  or  two  inches  in 
front  of  the  objective.  The  interior  of  the  instrument  is  then 
illuminated  by  diffuse  light.  If  now  the  reticule  is  closely  examined 
through  the  eyepiece,  a  slight  granular  deposit  may  be  detected. 
If  so,  the  film  is  beginning  to  form  and  may  be  expected  to  render  the 
instrument  useless  in  a  few  months  until  taken  apart  and  cleaned. 

If  the  telescope  is  of  the  binocular  type,  the  two  telescopes  should 
be  tested  independently  as  outlined  above.  It  should  be  further 
tested  by  fairly  continuous  use  for  an  hour  or  two  in  order  to  deter- 
mine whether  it  unduly  fatigues  the  eyes.  Sometimes  in  a  binocular 
the  mounting  is  not  correct  and  the  axes  of  the  telescope  are  not 
parallel.  If  the  instrument  is  of  the  prism  type,  the  prisms  may  be 
out  of  adjustment,  in  which  case  the  two  images  of  a  straight  line 
formed  by  the  two  telescopes  are  not  parallel.  Such  a  defect  is 
known  as  "twisted  field."  Either  of  these  two  defects  may  not  be 
noticed  if  the  instrument  is  used  but  a  short  time,  but  serious  eye 
strain  is  produced,  and  continued  use  is  very  fatiguing. 

The  mechanical  parts  should  work  smootlily  and  without  lost 
motion.  In  a  high-grade  binocular  instrument  an  adjustment 
should  be  provided  by  which  the  distance  between  the  two  eye- 
pieces may  be  varied  to  accommodate  the  iijterpupilary  distance  of 
different  observers.  The  two  telescopes  should  be  capable  of  inde- 
pendent focusing  in  order  to  secure  an  adjustment  for  differences 
which  may  exist  between  the  two  eyes. 

In  the  tests  described  above,  laboratory  methods  of  testing  have 
purposely  been  avoided.  Only  such  tests  have  been  described 
for  which  the  user  ordinarily  has  facilities.  If  a  complete  deter- 
mination of  the  optical  qualities  of  an  instrument  is  desired,  it 
may  be  sent  to  the  optical-instrument  department  of  the  Bureau 
of  Standards  for  test. 

THE    OPTICAL    CHARACTERISTICS    OF    SERVICE    FIRE-CONTROL 
INSTRUMENTS. 

Following  there  is  given  a  classification  of  the  different  fire-control 
instruments  based  upon  the  optical  systems  which  are  used.  A 
very  brief  description  of  the  more  salient  characteristics  of  the 
different  systems  is  given,  together  with  tables  giving  field  of  view, 
magification,  diameter  of  exit  pupil,  and  type  of  eyepiece  for  each 
instrument.  The  range  finder  has  been  omitted  and  is  described 
in  a  separate  section. 

The  telescopic  system  with  Porro  prisms. — In  figure  71  a  perspective 
view  is  shown  of  the  optical  system  commonly  employed  on  observa- 
tion telescopes  and  the  larger  telescopic  sights.  Erection  is  accom- 
plished by  means  of  a  Porro  prism  system  and  the  eyepiece,  in  most 
cases,   is  of  the  Kellner  type.     In   the  Longue-vue-Monoculaire  a 


74 


Porro  system  of  the  type  shown  in  figure  20  is  employed.  All  other 
instruments  have  the  type  illustrated  in  figure  19,  Below  is  tabu- 
lated the  optical  characteristics  of  the  instruments  in  which  this 
optical  system  is  employed : 


Telescopic  musket  sight,  model  1913. 
French  aiming  circle 

Maclune-giiii  panoramic  sight 

Azimuth  instrument,  model  1918 


Azimuth  instrument,  model  1910 

Observalion  telescope,  Longue-vue-Monoculaire. 


2-inch  telescopic  sight 

3-iQch  telescopic  sight 

Lewis  depression  position  iinder. 


Field  of        Magnifl- 
view.  cation. 


4  15 

11  20 

7  45 

3  50 

2  15 


G 

3.7 

5.9 
10 
20 
10 
15 
15 
23 
30 

8 
15 
15 
25 


Diameter 
of  exit 
pupil. 


0.14 
.15 
.17 
.25 
.12 
.30 
.20 
.20 
.13 
.10 
.25 
.20 
.20 
.12 


Type  of  eye- 
piece. 


Triple!  lei 
7''rencli. 
Kellner. 
Do. 

Do. 


French. 

Kellner. 
Do. 
Do. 
Do. 


EYE  LENS 
J)  LENS 


PORRO    PRISM 
ERECTING    SYSTEM 


r"iG.  71. — Telescope  with  Porro  erecting  system. 

The  telescopic  system  with  lens  erecting  system. — A  perspective  view 
of  the  telescopic  system  with  a  lens  erecting  system  is  shown  in 
figure  72.  This  optical  system  is  used  on  the  telescopic  tank  sight, 
the  new  musket  sight  and  the  telescopic  sight  for  the  37-mm.  infan- 
try gun.  For  the  last  two  sights,  the  system  is  substantially  as 
shown  in  the  drawing.  The  tank  sight  has  an  objective  relatively 
much  smaller  than  indicated  in  the  drawing  and  a  collective  lens  in 
the  plane  of  the  reticule.  The  optical  characteristics  of  the  different 
instruments  are  given  below : 


Instnmient. 

Field  of 
^^ew. 

38    30 
7    30 
7    25 

Magnifi- 
cation. 

Diameter 
of  exit 
pupil. 

Type  of  eye- 
piece. 

1.1 

2.5 
2.8 

0.16 
.20 

.25 

Do. 

Telescopic  sight  for  37-mm.  infantry  gun. 

Symmetrical. 

75 


The  periscopic  system. — The  periscopic  system  is  very  similar  to  the 
telescopic  system  %\ath  lens  erecting  system  shown  in  figure  72  with 
the  addition  of  two  right-angle  prisms.  The  complete  system  is 
shown  in  figure  73.  The  officer's  trench  periscope  and  battery  com- 
mander's periscope  are  the  two  instruments  in  which  this  optical 
system  is  employed. 


Instrument. 

Field  of 
view. 

Magnifi- 
cation. 

Diameter       rr.^^^f^„„ 
of  exit         ^^^°^^y^ 
pupil.               ^'^^• 

OflBcer's  trench  periscope  No.  10 

Battery  commander's  periscope 

5  15 

6  25 

!                i 

7      '             0.17  1  KeUner. 
5.7  ,              .2    1         Do. 

1 

The  periscopic  azimuth  instrument,  model  1918. — This  is  a  periscopic 
instrument  in  which  the  prisms  are  so  turned  that  the  observer  stands 
with  his  back  to  the  object  under  observation.  The  parts  of  a  single 
inverting  telescope  with  two  right-angle  prisms  are  employed.    Since 


0 


0  ® 

\y         LYE  lEN; 


Fig.  72. — Telescope  witti  leus  erecting  system. 

the  prisms  of  this  telescope  are  always  in  position  for  a  back  sight, 
erection  is  accomplished  by  the  prisms  without  the  addition  of  an 
erecting  system.     This  system  is  illustrated  in  figure  74. 


Tnstniment. 

Field  of 
view. 

Magnifi- 
cation. 

Diameter 
of  exit 
pupil. 

Type  of  eye- 
piece. 

6 

8 

0.22     KelLner. 

The  right-angle  telescope. — The  right-angle  telescope  is  showTi  in 
perspective  in  figure  75.  The  erection  of  image  and  the  bending  of 
the  axis  of  the  telescope  is  accomplished  by  a  single  prism,  a  90°  roof 
angle  prism. 

The  model  1918  antiaircraft  sight  uses  a  different  type  of  telescope, 
of  which  it  is  probable  that  no  more  will  be  constructed.  All  other 
types  of  antiaircraft  fire-control  apparatus  use  a  right-angle  tele- 
scope, as  shown  in  the  drawing.     The  optical  characteristics  of  the 


76 


OBJECTIVE    PRI5M 


obje:ctive 


COLLECTIVE    LENS 


^ 


ERECTING    5Y5TEM 


S^^®Yye  lens 
''^^       field  lens 
lower  reflecting  prism 


Fig.  73.— The  periscopic  .system. 


77 


OBJECTIVE   PRISM 


T^        OBJECTIVE 


Slower  reflecting  prism 


RETICULE 
eye  LENS   HELD    LENS 


Fig.  74.— Optical  system  of  the  periscopic 


azimuth  iiistrumeut,  Model  I'Jl 


78 


telescopes  for  all  instruments  are  substantially  the  same  and  are 
tabulated  below. 


Instrument. 

Field  of 
view. 

Magnifi- 
cation. 

Diameter 
of  exit 
pupil. 

Type  of  eye- 
piece. 

Right-angle  telescope 

9    45 

4.3 

O.IS 

French. 

OBJECTIVE 


EYE  LENS 
riELD  LENS 


RETICULE 


ROOF  PRISM 


Fig.  75.— The  right  anple  telescope. 

Tfie  'panoramic  telescope. — The  telescopic  system  employed  in 
panoramic  sights  is  shown  in  figure  76.  The  objective,  lower  re- 
flecting prism  and  eyepiece  are  similar  to  those  sho\\ai  in  figure  75 
for  the  right  angle  telescope.  Taken  together,  the}^  constitute  an 
erecting  telescope.  The  objective  prism  and  rotating  prism  when 
oriented,  as  shown,  deliver  to  the  telescope  an  erect  image  of  objects 
in  front  of  the  sight.  This  image  remains  erect  when  viewed  through 
the  telescope. 


79 


If  the  rotating  prism  remains  fixed  and  the  objective  prism  is 
rotated  in  azimuth  for  a  side  or  rear  sight,  the  image  viewed  through 
the  instrument  rotates  and  becomes  inverted  when  the  position  for 
a  back  sight  is  reached.     To  overcome  this  difficulty,  the  rotating 


PLANE   GLASS    WINDOW 


OBJECTIVE     PRISM 


ROTATING    PRI5M 


OBJECTIVE 


^'  '^  RETICULE 

LOVER  REELECTING  PRISM 


EYE  LENS 
FIELD   LEMS 


Fig.  76.— The  panoramic  telescni)e. 

prism  is  added.  The  rotating  prism  is  mechanically  connected  to 
the  objective  prism  by  gearing,  which  causes  it  to  rotate  with  half 
the  angular  velocity  of  the  objective  prism.  The  rotation  of  this 
lower  prism  serves  to  keep  the  image  in  a  vertical  position  regardless 
of  the  orientation  of  the  objective  prism. 


80 

This  optical  system  is  employed  in  the  4-power  panoramic  sight 
and  in  the  larger  4  and  10  power  panoramic  telescope  used  on  rail- 
way artillery.  Below  the  optical  characteristics  of  these  two  in- 
struments are  given : 


,  Instrument. 

Field  of 
view. 

Magnifi- 
cation. 

Diameter 
of  exit 
pupil. 

Type  of  eye- 
piece. 

Panoramic  sight,  4  power 

10    15 
8    20 
3    50 

4 
4 
10 

0.16 
.32 
.14 

S\Tnmetrical. 

Panoramic  telescope  4  and  10  power .   . 

Do. 

Binocular  telescopes. — Two  binocular  instruments  are  used  in  the 
Army,  the  service   binocular  (t3'pe  EE),  and  the  battery  command- 


EYE  LENS 


FIELD  LENS 
RETICULE 


PORRO   PRISM 
ERECTING  SYSTEM 


05JECTIVE 


Fig.  77.— Telescopic  system  of  field  glass. 

er's  telescope.  A  perspective  view  of  the  optical  system  of  the  type 
EE  binocular  is  shown  in  figure  77.  The  image  is  erected  by  Porro 
prisms.     The  reticule  is  in  the  left-hand  telescope. 

The  battery  commander's  telescope  is  a  large  binocular  instru- 
ment mounted  on  a  tripod.  The  two  telescopes  are  hinged  together 
and  can  be  used  in  two  positions.  When  turned  as  in  figure  78,  the 
instrument  serves  as  a  binocular  periscope  and  observations  can  be 
made  from  behind  a  parapet.  Both  arms  of  the  instrument  may 
be  swung  into  a  horizontal  position.  The  instrument  then  becomes 
an  excellent  stereobinocular  with  the  objectives  separated  approxi- 
matelv  27  inches. 


81 


The  erection  of  the  image  in  this  telescope  is  accompHshed  by  a 
modified  Porro  system  in  which  one  prism  is  replaced  by  two  right- 
angle  prisms  in  order  to  permit  the  first  reflection  to  take  place 
before  the  light  enters  the  objective.  The  reticule  is  in  the  left- 
hand  telescope.     Below  aile  given  the  optical  characteristics: 


lastnimer-t. 

Field  of 
view. 

Magnifi- 
cation. 

Diameter 
of  exit 
pupil. 

Type  of  eye- 
piece. 

8     0 
4    15 

6 

10 

0.19 
.17 

Kellner. 

Battery  commander's  telescope   

Do. 

OEUrCTiVE  PRISM 


OBJECTIVE 


.0EYE  LENS 
FIELD   LENS 


ERECTING     PRISMS 


Fig.  7S.— Telescopic  system  of  B.  C.  telescope. 

The  aiming  circle,  model  1916. — The  optical  system  shown  in  figure 
79  is  only  used  in  the  aiming  circle,  model  1916.  This  peculiar  type 
of  erecting  system  was  probably  employed  in  order  that  a  compact 

48918°— 21 6 


82 


telescope  might  be  constructed  which  takes  up  little  space  in  addition 
to  that  occupied  by  the  compass.  In  the  erecting  system  one  reflec- 
tion takes  place  at  a  silver  surface  and  this,  together  with  a  relatively 
lono-  light  path  and  large  number  of  surfaces,  results  in  a  large  absorp- 
tion of  light.  An  optical  system  of  this  type  probably  will  not  be 
employed  in  future  aiming  circles. 


Instrument. 

Field  of 
view. 

Magnifi- 
calion. 

Diameter 
of  exit 
pupil.  ^, 

Tj-pe  of  eye- 
piece. 

9    30 

3.9 

0.10 

Orthoscopic. 

OBJECTIVE    PRISM 


FIELD  LENS 
RETICULE 


ERECTING   PRISMS 


Fig.  79.— Optical  system  of  aiming  circle,  Model  1916. 

THE    COLLIMATOR. 

The  collimator  is  an  ingenious  and  inexpensive  type  of  sight  occu- 
pying a  position  intermediate  between  the  open  sight  and  the  tele- 
scopic. It  was  used  by  the  Germans  and  French  in  a  great  many 
places  on  their  fire-control  apparatus.  On  range  finders,  panoramic 
sights,  and  other  similar  instruments,  it  quite  generally  replaced  the 
auxiliary  open  sights  used  on  our  instruments.  Furthermore,  it  was 
the  fundamental  sighting  element  on  the  French  seventy-five.  The 
collimator  is  inferior  to  the  telescopic  sight  in  effectiveness  or  con- 
venience and  its  only  advantages  are  its  simplicity,  ruggedness,  and 
low  cost.  These  factors,  however,  make  its  use  particularly  desirable 
as  an  auxiliary  sighting  element. 


83 


The  principle  of  the  sight  is  ilhistrated  in  figure  80.  The  colhmator 
consists  essentially  of  an  opaque  reticule  bearing  a  transparent  cross, 
as  shown  at  D,  which  is  placed  in  the  focal  plane  of  a  converging  lens. 
The  assembled  view  is  shown  at  A  and  the  course  of  several  rays 
traced  which  proceed  from  the  intersection  of  the  two  arms  of  the 
cross.  Since  the  reticule  is  in  the  focal  plane,  the  rays,  after  passing 
through  the  lens,  are  parallel.  Therefore,  an  eye  placed  at  E,  F,  G, 
H,  or  I  wdll  see  the 
cross  in  a  fixed  direc- 
tion, i.  e.,  along  the 
respective  one  of  the 
several  parallel  rays. 
Consequentl}^,  as 
the  eye  is  moved 
from  side  to  side, 
the  direction  in 
which  the  cross  is 
located  remains  in- 
variant and  there  is 
no  parallax.  If  the 
collimator  is  not 
properly  adjusted, 
the    emergent   rays 

diverge  or  converge  as  shown  at  B  or  C.  As  the  eye  is  moved,  the 
direction  of  the  cross  shifts  and  there  is  parallax.  A  collimator 
which  shows  parallax  is  incorrectly  assembled  and  should  be  sent  to 
an  instrument  shop  for  readjustment. 

The  foreign-built  collimator  was  usually  constructed  as  shown  in 
figure  81.  The  light  path  is  almost  wholly  through  glass.  In  cross 
section,  the  dilTerent  elements  are  square.     Elements  A  and  B  are  of 


Fig.  so. — Diagrammatic  sketch  of  colhmator. 


Fig.  si.— The  coUimator. 

flint  and  C  is  made  of  cro^\Tl  glass.  This  lens  system  was  ^^Tapped  in 
paper  and  tightly  fitted  in  a  square  brass  tube.  This  type  of  system 
was  probably»selected  because  the  complete  elimmation  of  distortion 
is  secured  by  making  the  two  curved  surfaces  concentric.  Some  of 
the  American-made  collimators  were  constructed  exactly  like  the 
French  type  and  others  were  as  shown  in  figure  80.  During  the  war, 
only  two  sights  built  in  this  country  were  of  the  collimating  type,  the 
American-built  French  seventy-five  and  the  quadrant  siglit  used  on 


84 


the  37-mm.  gun.     Figure  81   illustrates  the  optics  of  the  French 
sight,  model  1901,  used  on  the  French  75-nim.  gun,  model  1897. 

Sighting  with  a  collimator  sight  is  generally  accomplished  by  one 
of  the  three  following-described  methods: 


Fig.  82.— The  correct  use  of  the  collimator  sight. 

Both  eyes  are  open  and  about  10  or  12  inches  from  the  cohimator. 
One  eye  sees  the  cross  through  the  collimator,  the  other  views  the 

target,  and  sighting  is  accomplished 
by  superposing  the  cross  on  the 
target.  This  method  is  funda- 
mentally incorrect,  as  it  is  only  accu- 
rate when  the  axes  of  the  two  eyes 
are  parallel.  Normally  the  axes  are 
____^__^___^_^^_  parallel    when    viewing    a    distant 

/^        ob  j  ec  t ,  but  the  intrusion  of  the  colli- 

^^^""^  yn  mator  mounting  in  the  field  of  view 

'  frequently  causes  the  axes  to  con- 

verge and  introduces  a  large  error. 
The  second  method  of  use  is 
similar  to  the  first  except  one  eye 
is  closed.  By  vertical  or  horizontal 
movement  of  the  head,  the  eye  is 
caused  to  view  successively  the  cross 
and  the  target.  The  sighting  is 
accomplished  in  a  manner  precisely 
analogous  to  that  in  which  one  lines 
up  three  stakes. 

The  third  method  is  indicated  in 
figure  82  and  is  the  most  precise  of 
all,  but  more  inconvenient  to  apply. 
The  eye  is  brought  directly  behind 
the  collimator  and  in  such  a  posi- 
tion that  the  lower  half  of  the  pupil 
receives  light  from  tRe  collimator, 
the  upper  half  from  the  target. 
The  cross  and  target  are  seen  simultaneously  and  aiming  is  satisfactory 
when  one  is  superposed  upon  the  other.  This  method  of  usmg  the 
collimator  is  much  facihtated  if  the  upper  part  of 
mounting  is  made  as  thin  as  possible. 


.—The  collimator  or  the  Michelin  sight. 


the  collimator 


85 

An  interesting  and  ingenious  elaboration  of  the  collimator  sight 
is  employed  in  the  Miehelin  bomb  sight.  The  optical  system  is.  illus- 
trated in  figure  83.  The  cube  of  glass  ABCD  is  made  up  of  two  pieces 
cemented  together  at  the  diagonal  surface  BD.  This  surface  carries 
a  thin  deposit  of  silver  so  thin  that  approximately  half  the  incident 
light  is  reflected  and  the  other  half  transmitted.  The  face  BC  bears 
the  reticule  design  transparent  upon  an  opaque  background.  The 
convex  surface  AD  is  silvered,  thus  forming  a  concave  reflector. 

Light  proceeds  from  the  reticule  toward  the  reflector.  A  portion 
of  this  light  is  reflected  do\\Tiward  by  the  half  silvered  face  BD  and 
is  not  utilized.  The  other  portion  reaches  the  reflector.  The  curva- 
tm-e  of  AD  is  so  selected  that  BC  is  in  the  focal  plane.  Therefore,  an 
image  of  B^is  formed  at  an  infinite  distance.  An  eye  looking  down- 
ward into  the  face  AB  sees  this  image  reflected  in  the  silver  surface 
DB.  Therefore,  the  observer  sees  Uie  image  of  the  reticule  projected 
and  magnified  in  the  direction  E(CJor  FH.  Furthermore,  since  the 
emergent  rays  are  parallel,  the  direction  in  which  this  image  is  seen 
is  independent  of  the  position  of  the  eye  and  there  is  no  parallax. 
But  at  the  same  time  that  the  eye  views  this  image  of  the  reticule 
it  also  sees  the  target  below  the  cube  by  the  light  which  proceeds  from 
the  target  and  passes  through  the  silver  film  at  DB.  Lines  IJ  and 
KL  show  the  path  of  such  rays.  Therefore  the  observer,  looking 
through  the  cube,  sees  the  target  and  the  reticule  superposed  upon 
it  without  parallax.  The  reticule  appears  as  a  network  of  bright 
lines  upon  the  relatively  dark  background  of  the  target. 

THE   COINCIDENCE-TYPE   SELF-CONTAINED    RANGE   FINDER. 

The   modern  horizontal   base   self-contained   range   finder   deter- 
mines the  range  by  a  method  of  triangulation.     The  base  line  is  con- 
tained in  the  instrument  and  by  reason  of  its  extreme  shortness  in 
comparison  with  the  range  to  be  determined,  the  accuracy  and  pre- 
^  r  r 


T 

.90° 


B 

Fig.  84. — The  fundamental  triangle  of  the  range  finder. 

cision  required  in  the  determination  of  the  angles  at  the  two  ends  of 
the  base  line  is  much  greater  than  that  afforded  by  other  instruments, 
with  the  exception  of  those  designed  for  the  most  exacting  laboratory 
requirements.  The  triangle  solved  by  the  range  finder  is  showTi  in 
figure  84.  AB  is  the  base  of  length  h,  C  the  target  and  AC  the  range 
r.     In  the  usual  construction,  the  base  length  and  angle  at  A  are 


86 


maintained  constant  in  value.  The  scale  upon  which  the  other 
angle  is  read  may  then  be  graduated  to  read  directly  in  range.  Al- 
thougli  the  instrument  is  graduated  to  read  in  linear  units,  it  must 
be  constantl;^  borne  in  mind  tliat  the  range  finder  is   fundamentally 

an  angle-measuring  instrument 
and,  in  a  study  of  the  errors  of  the 
instrument,  important  generali- 
zations can  be  made  and  conclu- 
sions drawn  much  more  readily  if 
the  errors  of  range  are  converted 
into  the  corresponding  angular 
errors. 

Since  the  angle  m  is  very  small, 

we  may  write  with  sufficient  accu- 

h 


racy  -  = 
transposing 

dr 


Differentiating  and 


-dm 


(49) 


and  we  have  the  relationship  ex- 
isting between  the  range  error  dr 
■  and  the  corresponding  angular 
*  error  dm.  In  the  horizontal  base 
range  finder,  as  used  by  the  Field 
Artillery,  the  base  length  is  1 
meter.  At  a  range  of  4,000  me- 
ters the  total  value  of  the  angle 
to  be  measured  is  50  seconds  and 
if  an  accuracy  of  2  per  cent  is  to 
be  secured,  the  value  of  this  angle 
must  be  determined  to  within  1 
second. 

In  an  attempt  to  obtain  a 
high  degree  of  precision  and  ac- 
curacy in  an  instrument  expected 
to  withstand  the  rough  usage 
of  service  conditions,  the  design 
and  construction  has  been  very 
carefully  worked  out  along 
novel  lines  which  differentiate 
this  instrument  completely  from 
all  other  angle-measuring  instruments.  It  would  be  impossible 
to  obtain  the  accuracy  required  if  the  observations  from  the 
two  ends  of  the  base  Ime  were  made  by  two  different  observers  or 
successively  by  a  single  observer.  Therefore,  one  of  the  most  strik- 
ing features  of  the  instrument  lies  in  the  fact  that  two  observations 


from  the  two  ends  of  the  base  are  made  simultaneously  by  a  single 
observer,  the  field  of  view  from  the  two  telescopes  being  viewed 
through  a  single  ocular  after  they  have  been  suitably  combined  by 
an  ocular  prism. 

Figure  85  is  a  diagrammatic  sketch  showing  the  fundamental 
parts  of  the  range  finder.  The  details  of  construction  have  been 
changed  in  some  instances  in  order  that  the  operation  may  be  more 
clearly  indicated  for  the  reader,  but  the  essential  parts  are  all  repre- 


M 


Fig.  86.— Erect  field. 


sented.  A  and  A'  are  two  penta  prisms  at  the  ends  of  the  base  line, 
by  wliicli  the  ra3's  of  light  are  directed  toward  the  ocular  prism 
sho\\Ti  diagrammatically  at  G.  B  and  B'  are  the  two  objectives. 
The  ocular  prism  functions  in  such  a  manner  that  at  H  there  is  a 
"divided  field,"  that  is,  the  field  is  divided  into  two  parts  b}-  a  sharp 
boundar}-  line.  The  image  in  one  part  of  the  field  is  that  produced 
by  rays  traversing  penta  prism  A  and  objective  B,  while  in  the  other 


N 


0 


Fig.  S7.— Invert  field. 


art  the  image  is  produced  by  A'  and  B'.     This  composite  field  is 
viewed  tlu-ough  the  eyepiece  J. 

Figures  86  and  87  show  two  types  of  such  a  divided  field.  That 
shoAvn  in  figure  86  is  known  as  the  erect  type.  At  K  the  field  is 
shown  when  "coincidence"  is  secured.  Except  for  the  presence  of  a 
dividing  line,  the  field  appears  as  though  formed  by  a  single  objective. 
At  L  the  same  type  of  field  is  shown  when  the  range  finder  is  not 
adjusted  for  coincidence.  In  figure  87  the  inverted  type  of  field  is 
represented  in  which  the  objects  in  the  upper  half  of  the  field  are  in- 


verted.  When  coincidence  is  secured  as  at  N,  the  image  in  the  upper 
half  is  the  same  as  would  be  obtained  if  the  image  in  the  lower  half 
were  mirrored  in  the  dividing  line.  At  O  the  field  is  not  adjusted  for 
coincidence. 

The  erect  type  of  field  is  usually  preferred  when  the  target  is  of  a 
regular  geometrical  shape,  with  well-defined  boundaries,  and  it  is, 
therefore,  commonly  used  by  the  Navy  and  Coast  Artillery  Corps. 
The  inverted  type  is  considered  to  have  advantages  when  the  target 
is  poorly  defined  or  very  irregular  in  shape,  and  is  consequently 
used  by  the  Field  Artillery  and  Infantry  where  the  objects  sighted 
upon  may  be  trees,  trench  parapets,  etc. 

Returning  to  figure  85,  if  prisms  C  and  E  are  not  present,  and  if 
the  instrument  is  symmetrically  and  perfectly  constructed,  so  that 
the  deviations  of  the  rays  at  all  reflecting  and  refracting  surfaces 
have,  their  nominal  values,  the  image  of  an  infinitely  distant  object 
presented  by  the  two  objectives  will  be  the  same,  and  in  the  field 
we  shall  have  coincidence,  as  indicated  at  K  or  N  (figs.  86  and  87). 
If  at  C  and  E  we  insert  two  prisms  of  glass  of  very  small  angle  and 
with  their  thicker  edges  turned  oppositely  we  shall  have  both  images 
shifted  slightly  in  the  focal  plane  in  the  same  direction  and  the 
coincidence  will  not  be  affected.  If  now  an  object  is  viewed  which 
is  within  the  useful  working  range  of  the  instrument,  the  two  images 
in  the  two  portions  of  the  divided  field  will  not  be  in  coincidence. 
If,  in  particular,  the  range  finder  is  rotated  in  a  horizontal  plane 
until  the  image  of  the  object  presented  by  A'  lies  in  the  center  of 
the  field,  the  image  presented  by  A  will  be  displaced  from  the  center, 

the  distance  ( tan  -  )  ./"  or  since  the  angle  —is  small,  the  displacement 

will  be  —  /,  where  h  is  the  base  length,  r  the  range  to  be  determined 
and /the  focal  length  of  the  objective  B.  If  the  prism  at  C  bends 
the  ray  through  the  angle  i  by  shifting  the  prism  in  the  appropriate 
direction  through  a  distance  .<?  so  that 

(50) 


s 

tan 

-\-f 

or  with  sufficient 

exactness 

si- 

A-f 

(51) 

the  image  may  be  brought  back  into  coincidence.  The  length  s 
through  which  the  prism  C  is  moved  is  then  a  measm-e  of  the  range, 
and  the  scale  along  which  C  moves  may  be  graduated  to  read  directly 
in  range.     The  graduations  will  be  marked  according  to  the  formula: 

s~U-i  (52) 

^    r 


89 

where  s  is  the  distance  of  the  graduation  for  range  /•  from  the  original 
position  of  the  prism  which  is  marked  infinity.  The  size  of  the 
instrument  and  rec{uirements  of  portabihty  usually  limit  the  yalue 
which  may  be  given  to  h  and  /.  so  that  by  making  i  the  angle  of 
deviation  produced  by  the  prism  C  very  small,  the  distance  between 
successive  graduations  may  be  increased  and  the  scale  made  as 
open  as  may  be  desired. 

It  will  be  noted  that  the  scale  is  a  reciprocal  one,  and  as  r  increases, 
the  distance  between  successive  graduations  for  a  given  increment 
in  r  decreases.  If  the  scale  were  graduated  to  read  the  angle  sub- 
tended at  the  target  by  the  base  of  the  instrument,  the  formula 
for  determining  the  graduations  is: 

s=i-m  (53) 

where  7n  is  the  angle  to  be  measured. 

The  wedge  at  E  provides  the  so-called  infinity  adjustment.  The 
effect  of  slight  deformations  due  to  stresses  originating  from  tem- 
perature changes  and  other  conditions  of  service  is  to  introduce 
errors  much  greater  than  the  instrumental  errors  of  the  range  finder. 
If  the  instrument  is  trained  on  an  object  at  a  known  range  wT:th  the 
prism  C  set  opposite  the  corresponding  reading  on  the  scale  at  D, 
there  should  be  coincidence  between  the  two  images  in  the  field. 
If  this  is  not  the  case,  coincidence  ma}^  be  secured  by  shifting  the 
prism  E.  The  range  finder  is  now  adjusted  so  as  to  be  accurate 
for  this  particular  range,  the  errors  due  to  the  slight  deformations 
having  been  compensated  by  the  shift  of  E.  After  the  scale  has 
been  justified  at  this  one  point,  if  the  instrument  has  been  correctly 
constructed  and  designed,  it  will  indicate  ranges  accurately  over 
the  entire  scale. 

The  known  range  commonly  selected  is  an  ''artificial  infinity" 
secured  by  the  use  of  a  ''measuring  lath"  or  some  type  of  internal 
adjustment,  and  for  this  reason  the  adjustment  of  prism  E  is  usually 
referred  to  as  the  infinity  adjustment.  On  some  types  of  instru- 
ments the  infinity  adjustment  is  provided  with  a  scale,  as  at  F, 
graduated  in  entirely  arbitrary  divisions  which  are  numbered. 
Tliis  enables  one  to  make  successively  several  independent  infinity 
adjustments  and  to  select  the  mean  as  read  on  the  scale  F  of  the 
several  readings  as  denoting  the  correct  adjustment. 

THE   CONSTRUCTION   OF   THE   RANGE    FINDER. 

The  particular  methods  of  construction  utilized  in  the  difTerent 
makes  of  range  finders  vary.  In  general,  the  infinity  adjustment  is 
not  accomplished  by  a  prism  as  shown  at  E  shifted  along  the  axis 
of  the  instrument.     Instead,  the  prism  is  commonly  placed  between 


90 

B'  and  A'  and  is  so  placed  that  the  plane  in  which  the  deviation 
takes  place  does  not  lie  in  the  plane  of  figure  85  but  at  an  angle  to  it. 
Then,  by  rotating  the  prism  about  the  axis  of  the  instrument,  the 
component  of  the  deviation  lying  in  the  plane  of  the  drawing  (the 
part  which  affects  the  coincidence)  may  be  varied  and  the  infinity 
adjustment  thus  secured.  In  the  Barr  &  Stroud  range  finder  the 
window  placed  in  front  of  A',  not  shown  in  figure  85,  is  slightly 
wedge-shaped  and  may  be  rotated  for  securing  the  desired  correction. 
In  the  Bausch  &  Lomb  range  finder,  the  longitudinal  movement 
of  C  is  obtained  by  connecting  C  with  a  spiral  thread  cut  on  the 
interior  of  a  collar  which  revolves  about  the  entire  optical  tube  of  the 
instrument.  The  range  scale  is  then  cut  in  a  spiral  on  the  outside 
of  this  collar.  This  enables  the  scale  to  be  made  very  long  and  open. 
On  the  Barr  &  Stroud  instrument  the  scale  D  is  attached  rigidly  to 


A  B  C 

Fig.  SS.— Rotating  prisms  used  in  the  range  finder. 

the  prism  and  moves  past  a  fixed    index.     A  window  in  the  outside 
tube  protected  by  glass  enables  the  scale  to  be  read. 

In  some  range  finders  a  prism  of  the  type  shown  at  C  in  figure  85 
is  not  employed  for  securing  coincidence.  Instead,  two  similar 
prisms  of  small  angle  are  mounted,  one  before  the  other,  as  shown  in 
section  in  figure  88.  They  are  connected  by  gearing  in  such  a  manner 
that  the  observer,  in  securing  coincidence,  causes  the  two  prisms  to 
rotate  through  equal  angles  in  opposite  directions.  \Ylien  the  prisms 
are  oriented  with  respect  to  each  other  as  at  B,  the  deviation  pro- 
duced by  one  prism  is  neutralized  by  the  other  and  there  is  no  de- 
viation. When  they  are  as  at  C,  the  maximum  deviation  is  produced 
and  for  intermediate  positions  the  deviation  has  intermediate  values. 
Such  a  combination  of  prisms  then  gives  a  deviation  which  is  con- 
stantly in  one  plane  and  which  may  be  caused  to  vary  from  zero  to  a 
maximum  value.  These  are  referred  to  as  rotating  wedges  or  rotating 
compensating  prisms.     Such  a  system  is  not  placed  at  C,  as  shown 


91 


in  figure  85,  but  is  placed  in  position  between  tbe  pent  a  prism  A  and 
the  objective  B. 

It  is  very  difficult  to  make  B  and  B'  so  that  they  have  precisely 
the  same  equivalent  focal  length.  If  they  difl'er,  coincidence  will  not 
be  independent  of  the  position  of  the  object  on  the  dividing  line. 
Frequently,  one  objective,  say  B,  is  made  of  longer  focal  length  than 
B',  and  a  second  lens  termed  an  "equal  magnification  lens"  is  placed 
between  B  and  the  focal  plane.  By  varying  the  distances  between 
the  two  lenses,  the  equivalent  focal  length  of  the  two  combined  may 
be  continuously  varied  until  equal  to  that  of  B'. 

There  are  numerous  varieties  of  ocular  prisms  in  use.  In  figure  89, 
there  is  shown  a  drawing  of  a  type  of  prism  found  in  the  1-meter  base 
invert-type  range  finder,  as  used  by  the  Field  Artillery.  Two  views 
of  the  prisms  are  shown.  In  the  first,  the  different  components  are 
separated  in  order 
that  the  different 
reflecting  surfaces 
may  be  seen  more 
clearly.  The  part 
Q  receives  the  light 
from  the  left-hand 
objective  and  after 
two  reflections,  the 
light  passes  upward 
to  the  eyepiece  at 
an  angle  of  approxi- 
mately 60°.  The 
rays  of  light  from 
the  right-hand  ob- 
jective after  two  reflection: 
ward  and  upward  by   prism   S. 


Fig.  89.— Ocular  prism. 


the  rhomb  R  are  reflected  for- 
It  should  be  noted  that  one  re- 
flection takes  place  on  the  lower  surface  of  S,  a  portion  of  which  is 
silvered.  It  is  the  boundary  of  this  silvered  region  which  forms  the 
dividing  line,  the  rays  which  are  not  intercepted  and  reflected  by  the 
silver  going  downward  and  never  entering  the  ocular.  On  the  other 
hand,  the  rays  from  the  left-hand  objective  which  strike  the  sflver 
are  reflected  do\vnward  and  do  not  enter  the  ocular.  The  prism  T 
cemented  on  the  inclined  portion  of  S  is  traversed  by  light  from  both 
objectives.  Its  purpose  is  to  equalize  the  length  of  light  path  for 
different  portions  of  any  beam  in  such  a  way  as  to  obviate  spectral 
dispersion. 

In  order  to  prevent,  so  far  as  possible,  any  relative  motion  between 
the  two  objectives  and  the  ocular  prism,  these  are  commonly  mounted 
in  a  substantial  inner  tube  termed  the  optical  tube.  Tliis  is  designed 
very  carefully  and  made  from  especially  selected  homogeneous  ma- 
terial in  order  that  the  detrimental  effect  of  temperature  changes 
may  be  nullified  so  far  as  possible.     Slight  displacements  of  the  penta 


92 


prisms  do  not  so  seriously  affect  the  accuracy  of  the  instrument  and 
they  are,  therefore,  carried  by  the  outer  tube.  The  outer  tube  is 
covered  with  heat  insulating  material,  in  order  to  protect  the  inner 
optical  tube  from  nonuniform  temperature  changes.  In  order  that 
slight  deformation  of  the  outer  tube  may  not  subject  the  optical  tube 
to  mechanical  stress,  the  two  are  connected  by  a  three-point  sus- 
pension. A  slight  displacement  of  one  tube  relative  to  the  other 
may  lead  to  an  appearance  in  the  field  as  shown  in  figures  86  and  87 
at  M  and  P,  where  the  dividing  line  cuts  the  two  images  at  different 
heights.  This  is  usually  spoken  of  as  an  error  in  the  halving  adjust- 
ment. Means  are  provided  for  bringing  the  dividing  line  back  to  its 
correct  position  by  shifting  the  inner  tube  relative  to  the  outer. 
By  inspection  of  the  figures  referred  to  above,  it  is  apparent  that  if 
any  object  accui'ately  perpendicular  to  the  dividing  line  is  used  for 
determining  the  coincidence,  as,  for  example,  the  mast  of  the  ship  in 
the  drawing,  a  small  error  in  the  halving  adjustment  introduces  no 
error  in  the  determination  of  coincidence.  If,  however,  a  sloping 
line  as  the  edge  of  the  sail  is  used  for  setting  coincidence,  the  error  is 
considerable. 

The  long  base-range  finders  used  by  the  Coast  Artillery  Corps  are 
provided  with  an  attachment  termed  an  '^  astigmatizer."  Two  small 
cylindrical  lenses  are  arranged  to  be  swung  into  the  paths  of  the  rays 
from  the  two  objectives  by  means  of  external  levers.  When  in  posi- 
tion, the  image  of  any  point  is  drawn  out  into  a  short  line  perpendicu- 
lar to  the  dividing  line,  (See  fig.  40.)  During  the  advance  of  a  hos- 
tile fleet  at  night,  the  best  target  available  may  be  a  searchlight. 
Without  the  astigmatizer,  range  taking  on  a  searchlight  would  require 
that  the  image  be  kept  exactly  on  the  dividing  line,  a  task  wliich 
would  prove  difficult.  With  the  astigmatizing  lenses  in  position,  the 
image  of  the  searchlight  is  a  short  line  and  the  training  of  the  range 
finder  does  not  have  to  be  done  so  accurately. 

In  the  following  table  there  is  given  in  tabulated  form  the  more 
important  optical  data  of  the  different  types  of  range  finder : 


Instrument. 

Branch  of  service. 

''■Ell?' 

Power. 

Field. 

Diameter 
of  exit 
pupil. 

80-centimeter  Bauscli  &   Lomb  azimuth 

type. 
80-centimeter  Bauseh  &  Lomb  fixed-base 

type. 
80-ccntimeter  Bauseh  &  Lomb  fixed  base 

with  internal  adjustment. 

Infantry 

do 

do 

do 

Invert 

...do 

...do 

...do 

11 

11 

11 

10 

15 
30 
30 

15 
28 
15 
28 
15 
28 
15 
2S 

4      0 

3    45 

3    45 

3    30 

3    10 
1    30 

1  30 

2  30 

1  20 

2  30 
1    20 
1     50 
1      5 
1     50 
1      5 

0.11 
.11 
.11 
.11 

manufactured  by  Keuffel  &  Esser. 
1-meter  Bauseh  &  Lomb  fixed  base 

Field  Artillery.. 
Coast  Artillery.. 

...do 

Erect 

...do 

.10 

.07 

.05 

KcufTel  &  Esser. 
12- foot  Bauseh  &  Lomb  fixed  base  with 

do 

do 

.13 

internal  adjustment. 

do 

...do 

.075 
.13 

internal  adjustment. 
20-foot  Bauseh  <V  Lomb  fixed  base  with 

internal  adjustment. 
.3fKfoot  Bauseh  ik  Lomb  fixed  base  with 

internal  adjustment. 

do 

do 

...do 

...do 

.075 
.13 
.075 
.15 
.079 

93 

The  large  number  of  prisms  in  the  optical  train  of  a  range  finder 
gives  rise  to  very  great  absorption  of  light.  The  variation  of  absorp- 
tion in  different  instruments  is  large,  as  so  much  of  the  light  path  is 
in  glass  that  a  relatively  slight  falling  off  of  the  transparency  of  the 
glass  increases  the  absorption  greatly.  Range  finders  which  have 
been  measured  show  a  transmission  as  great  as  39  per  cent  in  some 
cases,  while  in  particularly  poor  instruments  the  transmission  falls 
as  low  as  17  to  20  per  cent.  In  general,  the  absorption  for  the  two 
ends  of  a  single  instrument  differs  greatly  as  is  shown  by  the  fact 
that  one  of  the  fields  is  usually  visibly  darker  than  the  other. 

THE   AZIMUTH   TYPE   OF   COINCIDENCE   RANGE   FINDER. 

An  ingenious  modification  of  the  range  finder,  as  described  above, 
has  been  invented  by  Eppenstein  and  is  known  in  the  Army  as  the 
"azimuth  type"  of  instrument,  in  order  to  distinguish  it  from  the 
more  usual  form  wliich  in  contradistinction  is  termed  the  "  fixed-base" 
type.  Suppose  that  both  prisms  indicated  in  figure  85  are  omitted 
and  that  one  of  the  objectives  has  a  slightly  longer  focus  than  the 
other.  As  both  objectives  serve  a  common  eyepiece,  the  magnifica- 
tion of  the  two  ends  of  this  instrument  will  be  different.  Now,  if 
the  instrument  is  so  constructed  that  all  refractions  and  reflections 
take  place  in  the  nominal  manner,  the  image  of  an  object  at  an 
infinite  distance  will  still  remain  in  coincidence  at  the  center  of  the 
field.  In  general,  there  will  not  be  coincidence,  except  at  the  center, 
as  the  two  images  are  represented  to  different  scales  by  reason  of  the 
difference  in  magnification.  If  the  entire  instrument  is  rotated  in 
azimuth,  the  image  in  one  half  of  the  field  will  move  faster  than  in 
the  other  half,  since  the  magnifications  are  different.  Therefore,  if 
the  instrument  is  rotated  as  a  whole  in  the  proper  direction,  one 
image  vnW  overtake  the  other  and  coincidence  wiU  be  secured.  It 
will  be  shown  below  that  the  position  on  the  dividing  line  at  which 
coincidence  is  secured  is  a  function  of  the  range.  Consequently,  a 
scale  may  be  etched  on  the  prism  along  the  dividing  line  and  gradu- 
ated to  read  range  directly.  This  scale  will  appear  in  the  field  of  the 
instrument,  and  to  determine  the  range  it  is  only  necessary  to  rotate 
the  instrument  as  a  whole  in  azimuth  until  coincidence  is  secured. 
Then,  on  the  scale  opposite  the  point  on  the  dividing  line,  where 
coincidence  is  obtained,  the  correct  range  may  be  read. 

The  method  of  graduating  the  scale  is  as  follows:  Let/ and  f+Af 
be  the  focal  lengths  of  the  two  objectives.  Assume  that  the  instru- 
ment is  so  oriented  that  the  image  of  the  target  falls  in  the  center  of 
the  field  of  the  objective,  the  focal  length  of  which  is/4-  A/  Then,  if 
the  base  length  is  h  and  the  range  is  r  the  image  in  the  other  half  of  the 
field  is  displaced  from  the  center  in  the  focal  plane  through  the  linear 

distance   -^  •     If  we  turn  the  range  finder  m  azimuth  through  the 


94 


angle  Tc,  the  one  image  in  the  focal  plane  moves  a  linear  distance 
(/+  A/)  ^,  the  other  Jlc.  (The  angle  Ic  is  so  small  that  the  angle  is  sub- 
stituted for  tan  k.)     If  in  particular  Tc  is  so  chosen  that 

{f+M)l=fl-\-^  (54) 

the  one  image  will  have  overtaken  the  other  and  we  shall  have  coin- 
cidence.    Transposing  and  collecting  terms,  equation  54  becomes: 

(f+A{)]c  is  the  distance  from  the  center  at  which  coincidence  is  ob- 
tained.    If  we  denote  this  distance  by  I  we  have : 

l=(f+M)^_^i  (56) 

This  then  is  the  formula  by  which  we  can  construct  our  scale.  I  is 
the  distance  measured  from  the  center  of  the  field  for  the  graduation 
corresponding  to  any  range  r.  It  will  be  noted  that  the  scale  is  a  re- 
ciprocal one  and  that  for  a  given  base  length  the  distance  between 
graduations  increases  as  Af  is  decreased.  The  actual  length  of  the 
scale  is  limited  by  the  total  length  of  the  dividing  line  that  is  visible 
through  the  eyepiece.  In  an  instrument  constructed  as  described, 
only  half  of  this  length  could  be  utilized  for  a  scale  as  the  infinity 
point  from  which  the  graduations  begin  is  in  the  center  of  the  field. 
In  actual  construction,  the  infinity  adjustment  is  so  set  that  the  scale 
begins  at  the  extreme  edge  of  the  field. 

The  advantages  of  this  instrument  lie  in  its  simplicity  and  com- 
parative freedom  from  moving  parts  as  the  movable  prism  and  its 
mechanism  are  eliminated.  This  also  probably  enables  a  more  water- 
proof construction  to  be  utilized.  No  estimate  of  its  accuracy  as 
compared  with  the  fixed  base  type  of  instrument  is  available.  One 
possible  disadvantage  lies  in  the  fact  that  the  center  of  the  field  can 
not  be  used  for  all  ranges.  In  particular,  in  making  the  infinity 
adjustment,  coincidence  is  secured  at  the  extreme  edge  of  the  field 
when  conditions  are  most  unfavorable  as  regards  aberrations.  Nearly 
all  of  the  80-centimeter  base-range  finders  supplied  the  Infantry  are 
of  the  azimuth  type. 

THE   STEREOSCOPIC    RANGE   FINDER. 

The  stereoscopic  range  finder  difi^ers  fundamentally  from  the  coin- 
cidence range  finder  in  the  fact  that  both  eyes  are  used  and  range 
finding  is  accomplished  by  means  of  stereoscopic  vision.  In  its  sim- 
plest form  this  range  finder  is  a  large  stereobinocular  with  specially 
designed  reticules. 


95 


m 


O  LJ 


-ef 


A  schematic  sketch  is  shown  in  figure  90.  A,  B,  C,  D,  and  E  are 
respectively  penta  prism,  objective,  penta  prism,  reticule,  and  eye- 
piece of  one  telescope  of  the  binocular.  Corresponding  parts  of  the 
other  telescopes  are  at  A',  B',  C,  D',  and  E'.  As  a  result  of  the  high 
magnifying  power  and  the  large 
separation  of  the  penta  prisms,  a 
very  great  radius  of  stereoscopic 
vision  is  obtauied.  This  can  be 
computed  by  equation  44. 

The  range  finder  as  thus  far 
described  is  a  powerful  stereo- 
instrument  but  it  can  not  prop- 
erly be  called  a  range  finder,  as 
there  is  no  means  provided  for 
the  determination  of  range  other 
than  by  estimation.  It  is  con- 
verted into  a  range  finder  by  the 
addition  of  special  reticules  at  D 
and  D'.  Each  reticule  bears  a 
series  of  vertical  marks  arranged 
in  a  zigzag  pattern.  The  pat- 
terns on  the  two  reticules  differ 
in  precisely  the  same  manner  as 
the  two  halves  of  a  stereoscopic 
picture.  In  other  words,  the  two 
reticules  and  the  two  eyepieces, 
considered  separately,  constitute 
an  excellent  stereoscope  and  the 
images  on  the  two  reticules  viewed 
by  the  two  eyes  are  fused  into  a 
single  picture  appearing  in  stereo- 
scopic relief.  This  image  is  su- 
perposed upon  the  target.  Con- 
sequently, on  looking  into  the  in- 
strument, the  target  is  seen  in  en- 
hanced stereoscopic  relief  due  to 
the  long  base  AA'  and  superposed 
upon  it  are  the  marks  of  the  reti- 
cule, each  of  which  appears  by  vir- 
tue of  the  stereoscopic  effect  at  a 
different  distance  from  the  ob- 
server. Near  each  line  the  reticule 
carries  a  mark  indicating  its  ap- 
parent distance.  To  read  a  range  it  is  only  necessary  to  estimate  which 
mark  on  the  reticule  appears  to  be  at  the  same  distance  from  the 
observer  as  the  target.     The  number  near  the  mark  sives  the  range. 


O 


% 


o  UJ 


96 

In  a  second  type  of  range  finder,  the  observer  sees  only  a  single 
mark  in  the  field  of  view.  On  turning  a  roller,  as  in  the  ordinary- 
type  of  instrument,  the  mark  appears  to  advance  or  recede.  Adjust, 
ment  is  made  until  this  mark  apparently  coincides  with  the  target 
in  distance  as  well  as  angular  position.  The  range  is  then  read  on  a 
scale. 

At  present,  no  branch  of  the  service  is  using  the  stereo  range  finder 
This  type  of  instrument  possesses  certain  inherent  advantages  and 
disadvantages.  It  is  apparently  rather  well  established  that  the 
observers  who  are  to  use  a  stereoscopic  range  finder  must  be  care- 
fully selected  if  good  results  are  to  be  obtained,  as  the  stereoscopic 
effect  is  not  appreciated  with  equal  effect  by  all.  Careful  training  is 
also  necessary  before  accurate  readings  can  be  obtained.  This  also 
applies,  though  perhaps  not  with  equal  force,  to  the  coincidence 
range  finder.  For  a  sharply  defined  target  of  rectilinear  form,  as  the 
mast  of  a  ship,  a  steeple  or  similar  object,  the  coincidence  range 
finder  probably  gives  the  more  accurate  results.  For  irregularly 
shaped,  poorly  defined  objects,  as  clouds  of  smoke  or  clumps  of 
trees,  the  stereoscopic  range  finder  is  considered  by  some  authori- 
ties to  be  superior  to  the  coincidence  type.  No  reports  upon  recent 
tests  of  the  two  instruments  are  available  from  which  conclusions 
can  be  drawn.  As  the  field  of  the  stereoscopic  range  finder  is  free 
from  a  dividing  line,  it  is  an  ideal  observation  instrument.  It 
should  possess  real  advantages  in  determining  the  range  of  an  air- 
plane, as  the  difficulties  of  keeping  a  small  object  on  the  dividing 
line,  met  with  in  the  use  of  the  coincidence  type  of  finder,  are  avoided 

THE  ERRORS  OF  THE  RANGE  FINDER. 

The  more  important  errors  to  which  the  range  finder  .is  subject 
may  be  classified  under  the  two  following  heads:  (a)  Accidental 
errors  arising  from  inability  to  determine  coincidence  precisely, 
which  introduce  errors  proportional  to  the  square  of  the  range  and  to 
which  the  theory  of  errors  is  applicable;  (b)  systematic  errors  which 
introduce  errors  proportional  to  the  square  of  the  range  and  which 
can  be  completely  compensated  by  a  suitable  setting  of  infinity 
adjustment. 

(a)  Accidental  errors  arising  from  inahility  to  determine  coincidence 
precisely  and  whicJi  introduce  errors  'proportional  to  the  square  of  the 
range. — The  accidental  errors  depend  fundamentally  upon  the 
limitations  of  the  eye  and  the  quality  of  optical  performance  of  the 
range  finder.  Under  the  most  favorable  conditions,  when  two 
halves  of  an  image  separated  by  a  dividing  line,  are  presented  to  the 
eye  as  by  the  range  finder,  it  is  commonly  considered  that  the  proba- 
ble error  in  determining  coincidence  will  be  of  the  order  of  ten  or 
fifteen  seconds.  In  order  to  secure  round  numbers,  assume  that 
the  angular  error  is  12.4  seconds  which  corresponds  approximately 


97 

to  0.06    mil    or   0.00006  radian,   respectively.     This  is,   of    course, 

the  angular  error  in  the  apparent  field.     If  the  magnification  of  the 

instrument  is  a,  the  true  angular  error  in  the  fundamental  triangle 

of  measurement  corresponding  to  the  apparent  angular  error  in  the 

„  ,  ,     „    .  ,^,  ,      .    0.06     .,       0.00006      ,. 

field  of  view  of  the  ocularis mil  or radian. 

a  a 

We  shall  denote  this  angular  error  by  dm^.  It  should  be  emphasized 
that  the  value  as  given  above  gives  the  value  of  drrii  under  the  most 
favorable  conditions,  that  is,  a  trained  observer,  a  well  illuminated, 
sharply  defined  target  and  an  instrument  giving  excellent  definition. 
The  value  of  dm^  which  will  be  obtained  in  practice  is  a  function  of  the 
following  elements :  The  training  of  observer,  the  character  of  tai^et, 
the  condition  of  atmosphere  and  the  optical  performance  of  the 
range  finder.  A  bright,  well-illuminated  target,  presenting  weU- 
defined  contrasting  lines  on  which  the  setting  may  be  made  will  be 
much  more  favorable  for  range  finding  than  a  target  lacking  these 
features.  When  the  air  is  "boiling,"  the  irregular  refraction  makes 
exact  coincidence  difficult  to  obtain.  Excellent  definition,  high 
light  transmission  and  a  large  exit  pupil  may  all  be  considered  favor- 
able to  the  accurate  determination  of  coincidence. 

It  will  be  noted  that  the  value  of  dm^  is  independent  of  the  value 
of  m  which,  of  course,  depends  upon  the  range.  The  error  in  range 
corresponding  to  any  particular  value  of  dm^  is,  however,  not  inde- 
pendent of  the  range,  but  is  related  to  it,  as  shown  by  the  following 
equation: 

T^    d'Tfi 

The  1,000  is  introduced  in  the  denominator  in  order  that  din^  may 
be  expressed  in  mils.  The  magnifying  power  of  the  smaller  range 
finders  is  generally  from  12  to  15,  depending  upon  the  particular 
type.  The  larger  range  finders  have  two  eyepieces,  the  highest  of 
which  gives  a  magnification  of  28  and  can  only  be  used  under  very 
favorable  conditions.  If  the  magnification  is  15,  dm^  under  the  most 
favorable  conditions,  will  be  0.004  mil  or  0.000004  radian.  Under 
average  conditions,  dm^  may  be  expected  to  be  0.008  mil.  On  this 
basis,  the  table  following  is  computed  showing  errors  to  be  expected 
in  practice  with  range  finders  of  different  base  length.  If  the  28- 
power  eyepiece  is  used  on  the  large  instruments,  the  errors  may  be 
expected  to  be  approximately  50  per  cent  of  the  tabulated  values, 
48918°— 21 7 


98 


Error  in  yards. 

Range  in 

yards. 

SO-centi- 

1-meter 

9-foot 

15-foot 

22-foot 

30-foot 

meter  base. 

base. 

base. 

base. 

base. 

1,000 

9.1 

7.3 

2.7 

1.6 

1.1 

0.8 

2,000 

36.0 

29.0 

11.0 

r,.4 

4.4 

3.2 

3,000 

82.0 

66.0 

24.0 

14.0 

9.8 

7.2 

4.000 

140.0 

110.0 

43.0 

2,5.0 

17.0 

1.3.0 

5,000 

220.0 

180.0 

67.0 

40.0 

27.0 

20.0 

6,000 

320.0 

260.0 

96.0 

58.  0 

39.0 

29.0 

7,000 

440.0 

.360. 0 

130.0 

78.0 

53.0 

39.0 

8,000 

580.0 

470.0 

170.0 

100.0 

70.0 

51.0 

9,000 

740.0 

.590. 0 

220.0 

130.0 

88.0 

6.5.0 

10,000 

910.0 

730.0 

270.0 

160.0 

110.0 

80.0 

11,000 

1, 100. 0 

880.0 

320.0 

190.0 

130.0 

97.0 

12, 000 

1,300.0 

1, 100. 0 

380.0 

2.30.0 

160.0 

120.0 

13, 000 

1, 500. 0 

1,200.0 

450.0 

270.0 

180.0 

140.0 

14,000 

1,700.0 

1,400.0 

520.0 

310. 0 

210.0 

160.0 

15,000 

2,000.0 

1,600.0 

600.0 

360.0 

240.0 

180.0 

16,000 

2,300.0 

1,900.0 

680.0 

410.0 

2S0.0 

200.0 

17,000 

2,600.0 

2, 100. 0 

770.0 

460.0 

310.0 

230.  0 

18,000 

2,900.0 

2,400.0 

860.0 

.520. 0 

3.53.  0 

260.0 

19,000 

3,300.0 

2,600.0 

960.0 

580.0 

390.0 

290.0 

20,000 

3,600.0 

2,900.0 

1, 100. 0 

640.0 

440.0 

320.0 

21,000 

4,000.0 

3,200.0 

1,200.0 

700.0 

480.0 

350.0 

22,000 

4,400.0 

3,500.0 

1,300.0 

770.0 

530.0 

390.0 

23,000 

4,800.0 

3,900.0 

1,400.0 

850.0 

580.0 

420.0 

24,000 

5,200.0 

4,200.0 

1,500.0 

920.0 

630.0 

460.0 

25,000 

5, 700. 0 

4,600.0 

1,700.0 

1,000.0 

680.0 

500.0 

(b)  Systematic  errors  which  introduce  errors  proportional  to  the  square 
of  the  range  and  which  can  he  completely  compensated  hy  suitable  setting 
of  the  infinity  adjustment. — It  has  been  shouTi  in  the  preceding  para- 
graphs that  under  favorable  conditions  the  accidental  errors  of 
observation  may  be  as  small  as  0.004  mil  or  0.8  second.  This 
implies  a  remarkable  degree  of  accuracy  and  it  is  not  sm'prising  that 
under  service  conditions  the  parts  of  the  instrument  exposed  to 
mechanical  shock  and  heating  and  cooling  are  subject  to  relative 
displacements  and  deformations  which,  although  slight  when  con- 
sidered according  to  ordinary  standards,  are  nevertheless  sufficiently 
great  to  introduce  systematic  errors  too  great  to  be  neglected. 
Many  of  these  deformations  are  such  that  there  is  introduced  an  error 
dm^  in  the  measurement  of  m,  which  is  independent  of  the  value  of 
m  and  will,  therefore,  be  compensated  if  a  corresponding  opposite 
error  is  introduced  by  a  movement  of  the  adjusting  prism  E  shown 
on  figure  85.  For  example,  let  it  be  supposed  that  the  penta  prism 
A'  is  nonuniformly  heated  ^vnth  a  resultant  change  in  the  angle 
between  the  two  reflecting  surfaces  such  that  the  deviation  due  to 
penta  prism  A'  is  90°  4  dm.^  instead  of  the  normal  value  of  90°.  If 
now  the  prism  C  is  brought  opposite  a  graduation  corresponding  to 
any  particular  range,  and  the  range  finder  directed  at  an  object  at 
that  distance,  we  shall  in  general  not  have  coincidence  in  the  field 
of  the  ocular  because  of  the  incorrect  deviation  produced  by  A'. 
This  can  be  compensated  for  by  appropriately  shifting  E  along  the 
scale  -F,  so  that  an  equal  and  opposite  deviation  is  arbitrarily  intro- 


99 

duced.  Since  the  error  to  be  compensated  is  solely  due  to  A'  and 
does  not  vary  with  the  range  of  the  target,  the  error  when  com- 
pensated for  one  range  is  perfectly  compensated  for  all  other  ranges. 
It  is  readily  seen  that  if  there  are  several  errors  arising  from  different 
sources,  each  of  which,  like  the  one  dealt  with  above,  is  a  constant 
angular  error  independent  of  range,  the  net  result  of  all  the  errors 
can  be  compensated  by  a  single  shift  of  E.  Such  errors  may  be 
introduced  by  many  causes,  among  which  are  flexure  of  the  optical 
tube,  relative  displacement  of  the  objectives  at  right  angles  to  their 
common  axis,  displacement  of  ocular  prism,  or  unequal  heating  of  the 
optical  components.  The  adjustment  of  the  prism  E  may,  as  out- 
lined above,  be  made  by  selecting  an  object  at  a  known  distance  and 
making  the  adjustment.  As,  however,  objects  at  a  known  distance 
are  not  always  available,  recourse  is  usually  had  to  some  ingenious 
method  of  obtaining  two  parallel  pencils  of  light.  The  prism  C  is 
then  set  opposite  the  infinity  mark  and  the  prism  E  adjusted  until 
coincidence  is  obtained.  This  adjustment  is,  therefore,  termed  the 
infinity  adjustment.  If  the  infinity  adjustment  is  imperfectly  made, 
there  is  a  constant  error  dm^  introduced  and  to  this  there  corresponds 
a  range  error: 

dn=—-r~  dm^  (58) 

For  any  particular  faulty  infinity  adjustment,  introducing  a 
constant  angular  error  dm.,,  the  corresponding  error  dr^  will  always 
have  the  sign  and  magnitude  indicated  by  the  above  equation.  It 
will  be  noted  that  the  error  dr^,  unlike  dr^,  is  an  accidental  error  and 
is  as  likely  to  be  positive  as  negative.  Therefore,  under  the  most 
favorable  conditions,  the  reading  for  a  range  r  may  be  expected  to 
lie  between  r  +  dr^  +  dr.,  and  r  —  dr^  +  dr.,. 

THE    INFINITY   ADJUSTMENT   OF   THE    RANGE   FINDER. 

In  the  discussion  of  the  errors  of  the  range  finder  it  has  been  made 
apparent  that  a  range  finder  must  be  correctly  adjusted  if  accurate 
readings  are  to  be  secured.  Furthermore,  the  accuracy  of  angular 
measurement  required  of  the  range  finder  is  so  great  that  a  method  of 
adjustment  in  the  field  is  necessary  which,  if  possible,  should  be 
sufiiciently  convenient  to  permit  adjustment  immediately  before  the 
instrument  is  used. 

Adjustment  by  means  of  a  known  range  is  the  simplest  method. 
If  the  distance  to  a  suitable  target  is  given,  the  range  scale  on  the 
range  finder  is  set  to  this  known  value.  If  the  two  halves  of  the 
target  do  not  coincide,  they  are  brought  into  coincidence  by  means 
of  prism  E  (fig.  85).  The  range  finder  is  then  in  correct  adjustment. 
Under  service  conditions  a  known  range  is  not  ordinarily  available. 


100 

A  variant  of  this  method  depends  upon  the  use  of  a  celestial  body, 
for  which  the  moon  is  the  most  favorable.  The  range  scale  of  the 
range  finder  is  set  at  infinity  and  coincidence  secured,  as  before,  by 
movement  of  prism  E  (fig.  85).  The  sun  should  never  be  used  as 
a  target  for  adjusting  a  range  finder.  Even  though  one  should  be 
provided  with  a  filter  sufficiently  dense  to  protect  the  eye,  the  image 
of  the  sun  is  focused  upon  a  cemented  surface  of  the  ocular  prism  and 
is  likely  to  damage  the  instrument.  If  a  star  is  selected  as  the 
target,  the  astigmatizer  should  not  be  used  unless  previous  tests  show 
that  the  range  finder  gives  the  same  readings  yviih  or  without  the 
astigmatizer  in  the  light  path. 

Both  of  the  methods  of  adjustment  outlined  require  special  condi- 
tions for  their  application.     To  overcome  this  objection,  four  methods 

of  adjustment  depending  upon  the 
use  of  an  "artificial  infinity"  have 
been  developed  and  applied  to  range 
finders. 

The  most  simple  and  older  method 
of  adjustment  is  by  means  of  the  ad- 
justing lath  or  stadia.  One  of  the 
chief  disadvantages  of  this  method 
lies  in  the  fact  that  the  lath  is  not 
self-contained  in  the  instrument. 
Also,  it  is  not  always  convenient  to 
obtain  the  range  required  when  the 

vy rry      lath    is    to   be   used.     Accordingly, 

~^  ^     three  types  of  internal  adjustment 

'^  have  been  devised  which  form  an  in- 

FiG.  91.— The  adjusting  lath.  ^  ,  ,(■.!_•-  j.  j 

tegral  part  oi  the  instrument  and 
permit  adjustment  to  be  made  immediately  before  use. 

The  adjusting  lath  is  commonly  used  wath  the  smaller  base  range 
finder,  probably  because  of  its  portabiUty,  simplicity,  and  low-  cost. 
It  consists  of  a  simple  bar,  carrying  at  either,  end  a  target  w-hich  bears 
a  well-defined  black  line  upon  a  white  background.  These  black 
lines  should  be  the  same  distance  apart  as  the  actual  base  length  of 
the  range  finder.     The  method  of  use  is  illustrated  in  figure  91. 

A  and  B  represent  the  two  penta  prisms  at  the  ends  of  the  range 
finder,  and  C  and  D  the  black  lines  on  the  targets  at  the  ends  of  the 
adjusting  lath.  If  the  base  length  of  the  range  finder  is  the  same  as 
the  length  of  the  adjusting  lath,  and  if  CD  is  parallel  to  AB,  the  paths 
AC  and  BD  of  the  beams  of  light  are  accurately  parallel.  Conse- 
quently, if  the  scale  of  the  range  finder  is  set  at  the  infinity  mark  and 
the  adjusting  prism  E  (fig.  85)  moved  until  coincidence  is  secured  be- 
tween the  image  of  the  right  end  of  the  lath  in  one  field  and  that  of  the 
left  end  in  the  other,  the  correction  is  accomplished.     If  the  distance  CD 


101 


does  not  equal  AB,  an  angular  error  will  be  introduced,  the  value  ot 

,.  ^      .„  ,     AB-CD     .,  AB-CD  .       t.  ■ 

which  wdl  be  j^oqq^  mds  or  ocxTOOiTAC  ^®^°"^^-     ^^  ^^  apparent 

that  this  error  decreases  as  AC  is  increased,  and  the  instructions  of 
the  manufacturer  are  that  the  adjusting  lath  shall  be  set  at  a  dis- 
tance of  200  meters  or  more  from  the  range  finder.  However,  it  is 
not  improbable  that  conditions  may  arise  in  service  when  it  is  im- 
practicable to  use  as  great  a  distance,  and  accordingly  some  con- 
sideration will  be  given  to  the  use  of  an  adjusting  lath  at  distances  of 
50  and  100  meters. 

The  difference  in  length  may  be  an  apparent  one  due  to  lack  of 
parallelism  between  AB  and  CD  or  to  an  actual  difference  of  length 
which  may  be  due  to  an  initial  difference  of  length  between  AB  and 
CD  or  to  a  difference  of  length  brought  about  by  temperature 
changes.  In  order  to  avoid  the  foreshortening,  the  lath  should 
be  provided  with  an  efficient  sighting  device  by  which  parallelism 
can  be  secured  to  within  at  least  1°.  By  reference  to  a  table  of 
cosines,  it  can  be  seen  that  the  error  will  then  be  negligible  for  a 
range  finder  of  1  or  1^  meters  base  length.  In  addition,  each 
adjusting  lath  should  be  fitted  to  the  particular  range  finder  with 
which  it  is  to  be  used.  To  a  first  approximation  it  seems  that 
the  alteration  in  base  length  of  the  range  finder  mth  temperature 
will  be  due  to  the  increased  separation  of  the  penta  prisms  and 
a  result  of  the  expansion  of  the  outer  tube.  If  this  is  true, 
effects  due  to  a  common  rise  of  the  temperatm-e  of  range  finder  and 
lath  will  be  perfectly  compensated  by  making  outer  tube  of  range 
finder  and  the  measuring  lath  of  the  same  material. 

Below  is  given  a  table  showing  the  difference  in  length  between 
AB  and  CD  which  will  produce  an  error  of  1  second  in  the  adjustment 
for  three  distances  of  adjusting  lath  from  range  finder. 


Distance  of  ad- 
justing lath 
from  range 
finder. 

Length  produc- 
ing error  of 
0.005  mil. 

Meters. 
50 
100 
200 

Millimeters. 
0.25 
.50 
1.00 

It  will  be  noted  that  the  angular  error  produced  is  entirely  inde- 
pendent of  the  base  length.  The  range  error  is  connected  with  the 
angular  error  by  the  equation: 

r^    drn^ 
h   17)00 


7  /  Ulll. 

^^2=  ~r  Trin 


(59) 


The  value  of  the  range  errors  from  5,  000  and  1,000  yards  corre- 
sponding to  an  error  of  0.005  mil  and  for  a  1-meter  base  range  finder. 


102 


ai'e  resjpecthely  125  and  500  meters.  The  magnitude  of  these  errors 
makes  very  apparent  the  need  for  great  care  in  the  adjustment  of 
the  lath  to  the  particular  instrument  with  which  it  is  to  be  used. 

Figure  92  illustrates  a  type  of 
internal  adjuster  essentially  sim- 
ilar to  that  used  on  some  of  the 
Barr  &  Stroud  range  finders.  A 
and  B  are  two  small  penta  prisms 
mounted  directly  in  front  of  the 
large  prism.  C  and  D  are  two 
lenses,  the  focal  lengths  of  wliich 
are  identical  and  equal  to  the  sep- 
aration CD.  The  inner  face  of 
each  lens  has  etched  upon  it  a 
vertical  line.  The  small  prisms 
E  and  F  communicating  with  win- 
dows in  the  outer  tube  serve  to 
illuminate  the  etched  marks. 

Rays  proceeding  from  the  mark 
on  lens  C  are  rendered  parallel  by 
lens  D  and  enter  the  optical  sys- 
tem of  the  range  finder  proper  after 
having  been  bent  tlirough  ninety 
degrees  by  the  small  penta  prisms 
atB.  Since  the  bundle  of  rays  were 
rendered  parallel  by  lens  D,  the  im- 
age of  the  mark  is  seen  sharply 
defined  when  viewed  through  the 
range  finder  in  the  same  manner  as 
though  the  range  finder  were  actu- 
ally trained  on  an  object  at  a  great 
distance.  In  a  similar  manner  rays 
from  the  mark  on  lens  D  are  ren- 
dered parallel  by  lens  C  and  enter 
the  range  finder  at  the  other  end. 
Consequently,  on  looking  into  the 
range  finder  one  sees  the  one  mark 
in  the  upper  field,  the  other  in  the 
lower.  If  prisms  A  and  B  actually 
deviate  the  rays  through  ninety 
degrees,  the  two  bundles  of  rays  en- 
tering the  end  prisms  of  the  range 
finder  are  parallel.  Therefore,  if  the 
range  finder  scale  is  set  at  infinity,  the  images  of  the  two  marks  should 
coincide.  If  not  in  coincidence,  the  instrument  is  out  of  adjustment 
and  the  adjusting  prisms  must  be  altered  until  coincidence  is  secured. 


103 


^i 


It  should  be  noted  that  the  function  of  any  internal  adjustment  is 
to  deliver  to  the  range  finder  two  bundles  of  rays  which  shall  be  par- 
allel to  each  other  under  all  conditions.  By  ''all  conditions"  it  is 
meant  that  the  parallelism  must  be  maintained  so  far  as  possible 
regardless  of  the  distortion  of  the  system  produced  by  mechanical 
stresses  and  temperature  changes  to  which  the  instrument  is  inevi- 
tably subjected  in  service.  So 
far  as  possible,  the  optical  system 

of  the  internal  adjustment  must 

be  self-compensating.  Otherwise, 
the  conditions  which  put  the  range 
finder  out  of  adjustment  also 
render  the  internal  adjustment 
useless  as  a  standard  by  which  to 
readjust. 

The  seK-compensating  feature 
of  this  type  of  adjustment  lies  in 
the  fact  that  each  lens  bears  the 
mark  which  serves  as  a  target  for 
the  other  lens.  If,  for  example, 
lens  C  is  displaced  slightly,  the 
direction  of  the  bundle  of  rays  en- 
tering penta  prism  H  is  changed 
due  to  the  displacement  of  the 
vertical  mark  carried  by  C.  But 
at  the  same  time  the  direction  of 
the  bundle  entering  prism  G  is 
deviated  the  same  amount  since 
the  rays  entering  G  pass  through 
C.  Therefore,  parallelism  of  the 
two  bundles  of  rays  is  maintained 
independently  of  any  slight  lateral 
shift  of  lens  C  or  D.  If  then  the 
deviations  produced  by  prisms  A 
and  B  do  not  change,  the  adjuster 
will  function  satisfactorily.     As 

these  are  penta  prisms,  a  small     - 

movement  will  not  affect  the  de- 
viation. Nonuniform  heating  of 
either  of  these  prisms  might  introduce  an  error.  In  regard  to  this 
point,  the  manufacturers  assert  the  prisms  are  so  small  that  appreciable 
nonuniform  heating  is  unlikely  to  result. 

Previous  to  the  war,  a  small  lot  of  80  centimeter  base  range  finders 
were  purchased  from  Bausch  &  Lomb  having  an  internal  adjustment 
similar  to  that  shown  in  figure  93.  When  the  range  finder  is  to  be 
adjusted,  prisms  A  and  B,  which  are  normally  outside  the  path  of 


^'m-i 


^^ 


104 


the  light  rays,  are  swung  into  the  position  shown  in  the  drawing  by 
levers  on  the  outside  of  the  instrument.     These  prisms  are  of  the 

type  shown  in  figure  26. 

A  special  type  of  ocular  prism 
is  employed  which  bears  a  small 
index  mark  that  appears  in  the 
field  of  view.  A  window  is  pro- 
vided in  the  outer  tube  by  which 
this  mark  is  illuminated.  Rays 
proceeding  from  this  index  mark 
pass  to  the  right  tlirough  the 
wedge  and  the  objective.  The 
rays  are  then  deviated  through 
180°  by  the  triple  mirror.  A 
second  similar  triple  mirror  re- 
turns the  rays  to  the  left-hand 
objective  and  an  image  of  the 
index  mark  is  formed  in  the  field 
of  view.  The  course  of  the  rays 
is  indicated  by  the  arrows.  On 
looking  into  the  eyepiece  one 
sees  the  index  mark  in  one  field 
and  its  image  in  the  other.  Ad- 
justment is  accomplished  by  set- 
ting the  range  at  infinity  and 
bringing  image  and  index  mark 
into  coincidence  by  means  of 
the  adjusting  prism. 

The  self -compensating  feature 
of  this  adjuster  lies  in  the  fact 
that  the  deviation  produced  by 
a  triple  mirror  is  always  180°  ir- 
respective of  the  orientation  of 
the  prism.  If  the  triple  mirrors 
were  nonuniformly  heated  to 
such  an  extent  that  the  deviation 
produced  varies  from  the  normal 
value,  the  internal  adjuster  does 
not  function  correctly.  Further- 
more, it  will  be  noted  that  when 
adjustment  is  made,  the  two 
penta  prisms  are  not  in  the  path 
of  light.  Consequently,  any 
error  due  to  the  nonuniform 
heating  of  these  prisms  or  gradual  deformation  due  to  original  strain 
would  not  be  compensated  by  an  adjustment  accomplished  by  the 


105 

internal  adjuster.  It  is  hoped  that  tests  now  in  progress  will  show 
whether  the  errors  arising  from  these  sources  are  appreciable  in  the 
smaller  range  finders. 

The  large  range  finders  used  in  the  coast  defenses  are  equipped 
with  an  absolute  self-contained  adjusting  apparatus,  shoA\'n  in 
schematic  form  in  figure  94. 

B  and  C  are  two  small  penta  prisms  which  are  brought  into  position 
in  front  of  the  penta  prisms  of  the  range  finder  when  adjustment 
is  to  be  accomplished.  At  L  there  is  a  small  electric  lamp,  the  rays 
from  which  are  rendered  parallel  by  the  collimator  objective  at  A. 
This  portion  of  the  system  is  so  located  that  haK  the  rays  from  the 
collimator  are  intercepted  by  the  small  penta  prism  at  B  and  enter 
the  large  prism  of  the  range  finder.  The  other  half  passes  over  the 
prism  at  B  and  is  intercepted  by  the  rhomboid  prism.  (See  fig.  28.) 
This  rhomboid  prism  brings  the  beam  down  into  the  plane  of  the 


Fig.  95.— Method  of  internal  adjustment. 


penta  prism  at  C  and  the  half  of  the  beam  finally  enters  the  large 
penta  prism  to  the  left.  On  looking  into  the  eyepiece  one  sees  an 
image  of  the  light  at  L  in  both  fields.  The  range  scale  is  set  at 
infinity  and  coincidence  secured.  If  now  both  prisms  B  and  C  devi- 
ated the  rays  through  ninety  degrees,  adjustment  would  be  completed. 
But  in  general,  this  is  not  the  case. 

To  meet  this  difficulty,  a  second  collimator  indicated  by  the  dotted 
Unes  is  placed  at  the  other  end  of  the  range  finder.  The  light  at  L' 
is  turned  on  and  the  two  penta  prisms  are  swung  into  the  positions 
indicated  by  the  dotted  lines.  The  rhomboid  prism  at  D  is  also 
swung  through  180°.  Light  now  proceeds  from  L'  into  the  two  ends 
of  the  range  finder  and  adjustment  is  again  made.  In  general,  the 
setting  of  the  adjusting  prism  for  the  two  adjustments  will  not  be 
the  same.  The  adjusting  prism  is  provided  with  a  scale  and  a 
setting  intermediate  between  the  two  settings  gives  the  correct 
adjustment  for  the  range  finder. 


106 

The  accuracy  of  this  adjustment  does  not  depend  upon  the  magni- 
tude of  the  deviation  produced  by  the  two  small  penta  prisms  nor 
upon  the  parallelism  of  the  two  collimator  systems.  That  this  is  so 
is  apparent  on  reference  to  figure  95.  Using  the  right-hand  collimator 
and  with  the  penta  prisms  in  the  position  indicated  by  the  full  lines, 
the  course  of  the  rays  is  indicated  by  the  heavy  lines.  With  the 
left-hand  collimator  illuminated,  the  prisms  are  turned  as  sho\^^l  by 
the  dotted  hues  and  the  course  of  the  rays  is  indicated  by  the  light 
lines.  The  lateral  separation  of  the  two  positions  of  the  prism  is 
introduced  in  order  that  the  lines  of  the  drawing  may  not  be  con- 
fusing. Also  by  intention,  the  path  followed  by  rays  proceeding 
from  the  two  collimators  are  represented  considerably  out  of  parallel. 
With  one  setting  of  the  range  finder,  adjustment  is  made  on  rays 
OA  and  O'A',  from  the  other  setting  on  OB  and  O'B'.  It  is  evident 
that  neither  of  these  two  pairs  of  lines  are  parallel.  Therefore,  each 
adjustment  is  incorrect.  But  the  intermediate  setting  of  the  adjust- 
ing prism  is  equivalent  to  setting  on  the  bisectors  of  angles  AOB 
and  A'O'B'.  These  two  bisectors  are  parallel  in  all  cases,  as  is 
evident  from  the  geometry  of  the  drawing.  The  only  condition 
which  can  affect  the  accuracy  of  this  adjustment  is  a  change  in  the 
deviation  produced  by  any  component  which  should  develop  between 
the  two  successive  adjustments.  As  the  total  time  required  for  both 
adjustments  is  only  a  few  minutes,  this  lies  outside  the  bounds  of 
probability.  Tliis  method  of  adjustment  can  therefore  be  truthfully 
termed  an  absolute  adjustment.  This  self-contained  adjusting 
apparatus  is  much  too  complicated  for  introduction  into  the  smaller 
instruments  but  is  used  in  the  permanently  emplaced  long  base 
range  finders  used  by  the  Coast  Artillery  Corps. 

O 


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